@article{ito_liang_2024, title={A DIRECT PROBING METHOD OF AN INVERSE PROBLEM FOR THE EIKONAL EQUATION}, volume={46}, ISSN={["1095-7197"]}, DOI={10.1137/23M1577390}, abstractNote={.In this paper, we propose a direct probing method to solve the inverse problem of the Eikonal equation. This problem involves the determination of the inhomogeneous wave-speed distribution from first-arrival time data at measurement surfaces corresponding to distributed point sources. The viscosity solution of the point-source Eikonal equation represents the least traveltime of wave fields from the source to the point at the high-frequency limit. We show that this inverse problem is highly ill-posed. To address this issue, we develop a direct probing method that incorporates solution analysis of the Eikonal equation and several aspects of the velocity models. Specifically, we use the filtered back-projection method to reconstruct the inhomogeneous wave-speed distribution when it has a small variation from the homogeneous medium. For the scenarios involving high-contrast media, we assume a background medium and develop an adjoint-based back-projection method to identify the variations of the medium from the assumed background.KeywordsEikonal equationstraveltime tomographydirect probing methodMSC codes65K1086A2294A08}, number={2}, journal={SIAM JOURNAL ON SCIENTIFIC COMPUTING}, author={Ito, Kazufumi and Liang, Ying}, year={2024}, pages={A1235–A1251} }
@article{liu_zhao_ito_zhang_2023, title={Error estimates of Fourier finite volume element method for parabolic Dirichlet boundary optimal control problems on complex connected domains}, volume={186}, ISSN={["1873-5460"]}, DOI={10.1016/j.apnum.2023.01.007}, abstractNote={In this paper, we study the parabolic Dirichlet boundary optimal control on complex connected domains. It is well known that both the complex connected domain and the Dirichlet boundary control bring great difficulties to theoretical analysis and numerical calculation. The complex connected domain is a typical non-convex domain, and it is difficult for the traditional numerical method to obtain the same convergence order as the state and adjoint state for the Dirichlet boundary control. The optimal system of the proposed control problem is first obtained by using Lagrange multiplier method. Then, based on the variational form, the Fourier finite volume element method is used to obtain the fully discrete scheme of the optimality system, that is, using Fourier expansion method in azimuthal direction and applying finite volume element method in radial direction respectively, and the Crank-Nicolson scheme in the time direction. Next, we strictly prove the error estimates of state, adjoint state and Dirichlet boundary control by using the variational discretization concept. Finally, the theoretical analysis results and the feasibility and effectiveness of the proposed method are verified by numerical experiments.}, journal={APPLIED NUMERICAL MATHEMATICS}, author={Liu, Wenju and Zhao, Tengjin and Ito, Kazufumi and Zhang, Zhiyue}, year={2023}, month={Apr}, pages={164–201} }
@article{ito_liang_zou_2022, title={Least-squares method for recovering multiple medium parameters}, volume={38}, ISSN={["1361-6420"]}, DOI={10.1088/1361-6420/ac999a}, abstractNote={Abstract
We present a two-stage least-squares method for inverse medium problems of reconstructing multiple unknown coefficients simultaneously from noisy data. A direct sampling method is applied to detect the location of the inhomogeneity in the first stage, while a total least-squares method with a mixed regularization is used to recover the medium profile in the second stage. The total least-squares method is designed to minimize the residual of the model equation and the data fitting, along with an appropriate regularization, in an attempt to significantly improve the accuracy of the approximation obtained from the first stage. We shall also present an analysis on the well-posedness and convergence of this algorithm. Numerical experiments are carried out to verify the accuracies and robustness of this novel two-stage least-squares algorithm, with high tolerance of noise in the data.}, number={12}, journal={INVERSE PROBLEMS}, author={Ito, Kazufumi and Liang, Ying and Zou, Jun}, year={2022}, month={Dec} }
@article{chung_ito_yamamoto_2022, title={Least squares formulation for ill-posed inverse problems and applications}, volume={101}, ISSN={["1563-504X"]}, DOI={10.1080/00036811.2021.1884228}, abstractNote={In this paper we propose a least squares formulation for ill-posed inverse problems. For example, ill-posed inverse problems in partial differential equations are those such that a solution of inverse problem exists for a smooth data but it does not depend continuously on data, or there is no solution for inverse problem, e.g. the Cauchy problem for elliptic equations and backward solution of parabolic equations. We develop the least squares formulation in which the sum of equations error over domain and data fitting criterion and Tikhonov regularization terms is minimized over entire solutions. In this way we can establish the existence and uniqueness of an inverse solution and establish the continuity of the inverse solution for noisy data in . The method can be applied to a general class of non-linear inverse problems and an operator theoretic stability analysis is developed. We describe how one can apply the method for various PDE inverse problems. Numerical tests using backward heat equation and Cauchy problem for elliptic equations are presented to demonstrate the applicability and performance of the proposed method.}, number={15}, journal={APPLICABLE ANALYSIS}, author={Chung, Eric and Ito, Kazufumi and Yamamoto, Masahiro}, year={2022}, month={Oct}, pages={5247–5261} }
@article{zhao_ito_zhang_2021, title={Semi-decoupling hybrid asymptotic and augmented finite volume method for nonlinear singular interface problems}, volume={396}, ISSN={["1879-1778"]}, DOI={10.1016/j.cam.2021.113606}, abstractNote={An accurate semi-decoupling numerical method has been proposed for nonlinear singular differential equation with interface, which combines Puiseux series asymptotic technique with augmented compact finite volume method. The main motivation is to decouple the singular interface problem and get high order accurate numerical solution. Key to our proposed new method is introducing three augmented variables involving the interface and the singularity, and reconstructing the representative of the solution as the Puiseux series expansions on the interface to decouple original problem as two standard nonlinear singular problems with the second jump condition. In this way, the augmented variables related with semi-analytic solutions near the interface and numerical solutions can be simultaneously solved in the remaining interval on both sides of the interface. It demonstrates that our method does not take more heavier works for handling jump conditions like other methods, and is independent of the interface and jump ratio. A rigorous error estimate for the solution of nonlinear singular differential equation with interface and augmented variables is obtained. Numerical experiments for those singular differential equations with interface confirm the theoretical analysis and accuracy of the new approach. In particular, an interesting example with blow-up coefficient at singular point shows that our approach can be extended to numerically solve strongly singular interface problem.}, journal={JOURNAL OF COMPUTATIONAL AND APPLIED MATHEMATICS}, author={Zhao, Tengjin and Ito, Kazufumi and Zhang, Zhiyue}, year={2021}, month={Nov} }
@article{ito_reisinger_zhang_2021, title={A Neural Network-Based Policy Iteration Algorithm with Global H-2-Superlinear Convergence for Stochastic Games on Domains}, volume={21}, ISSN={["1615-3383"]}, DOI={10.1007/s10208-020-09460-1}, abstractNote={AbstractIn this work, we propose a class of numerical schemes for solving semilinear Hamilton–Jacobi–Bellman–Isaacs (HJBI) boundary value problems which arise naturally from exit time problems of diffusion processes with controlled drift. We exploit policy iteration to reduce the semilinear problem into a sequence of linear Dirichlet problems, which are subsequently approximated by a multilayer feedforward neural network ansatz. We establish that the numerical solutions converge globally in the $$H^2$$
H
2
-norm and further demonstrate that this convergence is superlinear, by interpreting the algorithm as an inexact Newton iteration for the HJBI equation. Moreover, we construct the optimal feedback controls from the numerical value functions and deduce convergence. The numerical schemes and convergence results are then extended to oblique derivative boundary conditions. Numerical experiments on the stochastic Zermelo navigation problem are presented to illustrate the theoretical results and to demonstrate the effectiveness of the method.}, number={2}, journal={FOUNDATIONS OF COMPUTATIONAL MATHEMATICS}, author={Ito, Kazufumi and Reisinger, Christoph and Zhang, Yufei}, year={2021}, month={Apr}, pages={331–374} }
@article{king_ito_hodyss_2020, title={A numerical integration-based Kalman filter for moderately nonlinear systems}, volume={72}, ISSN={["1600-0870"]}, DOI={10.1080/16000870.2020.1712938}, abstractNote={Abstract This paper introduces a computationally efficient data assimilation scheme based on Gaussian quadrature filtering that potentially outperforms current methods in data assimilation for moderately nonlinear systems. Moderately nonlinear systems, in this case, are systems with numerical models with small fourth and higher derivative terms. Gaussian quadrature filters are a family of filters that make simplifying Gaussian assumptions about filtering pdfs in order to numerically evaluate the integrals found in Bayesian data assimilation. These filters are differentiated by the varying quadrature rules to evaluate the arising integrals. The approach we present, denoted by Assumed Gaussian Reduced (AGR) filter, uses a reduced order version of the polynomial quadrature first proposed in Ito and Xiong [2000. Gaussian filters for nonlinear filtering problems. IEEE Trans. Automat. Control. 45, 910–927]. This quadrature uses the properties of Gaussian distributions to form an effectively higher order method increasing its efficiency. To construct the AGR filter, this quadrature is used to form a reduced order square-root filter, which will reduce computational costs and improve numerical robustness. For cases of sufficiently small fourth derivatives of the nonlinear model, we demonstrate that the AGR filter outperforms ensemble Kalman filters (EnKFs) for a Korteweg-de Vries model and a Boussinesq model.}, number={1}, journal={TELLUS SERIES A-DYNAMIC METEOROLOGY AND OCEANOGRAPHY}, author={King, Sarah A. and Ito, Kazufumi and Hodyss, Daniel}, year={2020}, month={Jan} }
@article{heikkola_ito_toivanen_2019, title={A PARALLEL DOMAIN DECOMPOSITION METHOD FOR THE HELMHOLTZ EQUATION IN LAYERED MEDIA}, volume={41}, ISSN={["1095-7197"]}, DOI={10.1137/18M1230906}, abstractNote={An efficient domain decomposition method and its parallel implementation for the solution of the Helmholtz equation in three-dimensional layered media are considered. A modified trilinear finite el...}, number={5}, journal={SIAM JOURNAL ON SCIENTIFIC COMPUTING}, author={Heikkola, Erkki and Ito, Kazufumi and Toivanen, Jari}, year={2019}, pages={C505–C521} }
@article{arridge_ito_jin_zhang_2018, title={Variational Gaussian approximation for Poisson data}, volume={34}, ISSN={["1361-6420"]}, DOI={10.1088/1361-6420/aaa0ab}, abstractNote={The Poisson model is frequently employed to describe count data, but in a Bayesian context it leads to an analytically intractable posterior probability distribution. In this work, we analyze a variational Gaussian approximation to the posterior distribution arising from the Poisson model with a Gaussian prior. This is achieved by seeking an optimal Gaussian distribution minimizing the Kullback–Leibler divergence from the posterior distribution to the approximation, or equivalently maximizing the lower bound for the model evidence. We derive an explicit expression for the lower bound, and show the existence and uniqueness of the optimal Gaussian approximation. The lower bound functional can be viewed as a variant of classical Tikhonov regularization that penalizes also the covariance. Then we develop an efficient alternating direction maximization algorithm for solving the optimization problem, and analyze its convergence. We discuss strategies for reducing the computational complexity via low rank structure of the forward operator and the sparsity of the covariance. Further, as an application of the lower bound, we discuss hierarchical Bayesian modeling for selecting the hyperparameter in the prior distribution, and propose a monotonically convergent algorithm for determining the hyperparameter. We present extensive numerical experiments to illustrate the Gaussian approximation and the algorithms.}, number={2}, journal={INVERSE PROBLEMS}, author={Arridge, Simon R. and Ito, Kazufumi and Jin, Bangti and Zhang, Chen}, year={2018}, month={Feb} }
@article{ito_kunisch_2016, title={A SEQUENTIAL METHOD FOR A CLASS OF STABLE MATHEMATICAL PROGRAMMING PROBLEMS}, volume={26}, ISSN={["1095-7189"]}, DOI={10.1137/140985597}, abstractNote={A sequential programming method of first order for constrained optimization in infinite dimensional spaces is presented. It is referred to as the SP method. It relies on Lipschitz stability of the minimizers with respect to perturbations in an essential way, and is motivated by optimal control problems with partial differential equations as constraints. Convergence and convergence rate are analyzed based on solutions of first order optimality conditions and on Lagrange multiplier theory. The first order SP method does not rely on an approximation of the Hessian of the Lagrange functional and consequently it avoids instabilities due to possible indefiniteness far from a local minimum. It is especially well suited for bilinear control problems and can be extended to certain classes of nonsmooth and convex problems. It can efficiently be implemented by the use of saddle point solvers, with complexity which is between that of gradient and SQP methods. For the important class of bilinear control problems the m...}, number={2}, journal={SIAM JOURNAL ON OPTIMIZATION}, author={Ito, Kazufumi and Kunisch, Karl}, year={2016}, pages={1262–1292} }
@article{chow_ito_zou_2016, title={ANALYSIS ON A NONNEGATIVE MATRIX FACTORIZATION AND ITS APPLICATIONS}, volume={38}, ISSN={["1095-7197"]}, DOI={10.1137/15m1020824}, abstractNote={In this work we perform some mathematical analysis on a special nonnegative matrix trifactorization (NMF) and apply this NMF to some imaging and inverse problems. We will propose a sparse low-rank approximation of positive data and images in terms of tensor products of positive vectors and investigate its effectiveness in terms of the number of tensor products to be used in the approximation. A new multilevel analysis (MLA) framework is suggested to extract major components in the matrix representing structures of different resolutions but still preserve the positivity of the basis and sparsity of the approximation. We will also propose and formulate a semismooth Newton method based on primal-dual active sets for the nonnegative factorization. Numerical results are given to demonstrate the effectiveness of the proposed method at capturing features in images and structures of inverse problems under no a priori assumption on the underlying structure in the data as well as to provide a sparse low-rank repres...}, number={5}, journal={SIAM JOURNAL ON SCIENTIFIC COMPUTING}, author={Chow, Yat Tin and Ito, Kazufumi and Zou, Jun}, year={2016}, pages={B645–B684} }
@article{king_kang_ito_2016, title={Reduced Order Gaussian Smoothing for Nonlinear Data Assimilation}, volume={49}, ISSN={["2405-8963"]}, DOI={10.1016/j.ifacol.2016.10.163}, abstractNote={We investigate Gaussian filtering for data assimilation in numerical weather prediction (NWP). Data assimilation is the process of combining prior forecasts and observations to produce a system estimate. The prevailing data assimilation method in operational NWP centers is variational data assimilation. This method involves solving a cost function over a time window forming a maximum likelihood estimate. This method, however, requires the use of linearized models which in practice are difficult to produce and maintain. As an alternative we propose Gaussian smoothing for derivative-free, nonlinear data assimilation. Gaussian filters and their corresponding smoothers use numerical integration to evaluate the recursive Bayesian formulas for optimal filtering under Gaussian assumptions. This numerical integration typically requires many model evaluations making conventional Gaussian filtering/smoothing impractical for use in NWP. We will present a reduced order method for forming a Rauch-Tung-Striebel (RTS) type smoother. To do so we review the Bayesian filtering and smoothing equations and discuss an efficient numerical method for evaluating them. We will then discuss a numerical example using the Korteweg-de Vries equation to compare our technique to the standard variational approach.}, number={18}, journal={IFAC PAPERSONLINE}, author={King, Sarah A. and Kang, Wei and Ito, Kaztifurni}, year={2016}, pages={199–204} }
@article{ito_landi_2016, title={THE NONNEGATIVE MATRIX FACTORIZATION: REGULARIZATION AND COMPLEXITY}, volume={38}, ISSN={["1095-7197"]}, DOI={10.1137/14099841x}, abstractNote={Data continues to grow, and it has become ever important to find effective big data analysis techniques. Computational tools, such as singular value decomposition, have been employed in the interpretation of big data. Another tool has recently gained popularity and comparative success: the nonnegative matrix factorization (NMF). The NMF method is a feature selection, dimension reduction algorithm which takes a data matrix and finds a simpler representation. In this paper, we discuss the choice of regularization parameters for a regularized NMF problem, and we develop a primal-dual active set method which enhances the representation. In addition, we examine rank determination for the case of the NMF problem. We develop a method to choose the proper complexity based on the concept of NMF-singular values.}, number={2}, journal={SIAM JOURNAL ON SCIENTIFIC COMPUTING}, author={Ito, K. and Landi, A. K.}, year={2016}, pages={B327–B346} }
@article{clason_ito_kunisch_2016, title={A CONVEX ANALYSIS APPROACH TO OPTIMAL CONTROLS WITH SWITCHING STRUCTURE FOR PARTIAL DIFFERENTIAL EQUATIONS}, volume={22}, ISSN={["1262-3377"]}, DOI={10.1051/cocv/2015017}, abstractNote={Optimal control problems involving hybrid binary-continuous control costs are challenging due to their lack of convexity and weak lower semicontinuity. Replacing such costs with their convex relaxation leads to a primal-dual optimality system that allows an explicit pointwise characterization and whose Moreau–Yosida regularization is amenable to a semismooth Newton method in function space. This approach is especially suited for computing switching controls for partial differential equations. In this case, the optimality gap between the original functional and its relaxation can be estimated and shown to be zero for controls with switching structure. Numerical examples illustrate the effectiveness of this approach.}, number={2}, journal={ESAIM-CONTROL OPTIMISATION AND CALCULUS OF VARIATIONS}, author={Clason, Christian and Ito, Kazufumi and Kunisch, Karl}, year={2016}, pages={581–609} }
@article{chow_ito_liu_zou_2015, title={DIRECT SAMPLING METHOD FOR DIFFUSIVE OPTICAL TOMOGRAPHY}, volume={37}, ISSN={["1095-7197"]}, DOI={10.1137/14097519x}, abstractNote={In this work, we are concerned with the diffusive optical tomography (DOT) problem in the case when only one or two pairs of Cauchy data is available. We propose a simple and efficient direct sampling method (DSM) to locate inhomogeneities inside a homogeneous background and solve the DOT problem in both full and limited aperture cases. This new method is easy to implement and less expensive computationally. Numerical experiments demonstrate its effectiveness and robustness against noise in the data. This provides a new promising numerical strategy for the DOT problem.}, number={4}, journal={SIAM JOURNAL ON SCIENTIFIC COMPUTING}, author={Chow, Yat Tin and Ito, Kazufumi and Liu, Keji and Zou, Jun}, year={2015}, pages={A1658–A1684} }
@article{ackleh_chellamuthu_ito_2015, title={FINITE DIFFERENCE APPROXIMATIONS FOR MEASURE-VALUED SOLUTIONS OF A HIERARCHICALLY SIZE-STRUCTURED POPULATION MODEL}, volume={12}, ISSN={["1551-0018"]}, DOI={10.3934/mbe.2015.12.233}, abstractNote={We study a quasilinear hierarchically size-structured population model presented in [4]. In this model the growth, mortality and reproduction rates are assumed to depend on a function of the population density. In [4] we showed that solutions to this model can become singular (measure-valued) in finite time even if all the individual parameters are smooth. Therefore, in this paper we develop a first order finite difference scheme to compute these measure-valued solutions. Convergence analysis for this method is provided. We also develop a high resolution second order scheme to compute the measure-valued solution of the model and perform a comparative study between the two schemes.}, number={2}, journal={MATHEMATICAL BIOSCIENCES AND ENGINEERING}, author={Ackleh, Azmy S. and Chellamuthu, Vinodh K. and Ito, Kazufumi}, year={2015}, month={Apr}, pages={233–258} }
@article{zhang_ito_li_zhang_2015, title={Immersed finite elements for optimal control problems of elliptic PDEs with interfaces}, volume={298}, ISSN={["1090-2716"]}, DOI={10.1016/j.jcp.2015.05.050}, abstractNote={This paper presents a numerical method and analysis, based on the variational discretization concept, for optimal control problems governed by elliptic PDEs with interfaces. The method uses a simple uniform mesh which is independent of the interface. Due to the jump of the coefficient across the interface, the standard linear finite element method cannot achieve optimal convergence when the uniform mesh is used. Therefore the immersed finite element method (IFEM) developed in Li et al. [20] is used to discretize the state equation required in the variational discretization approach. Optimal error estimates for the control, state and adjoint state are derived. Numerical examples are provided to confirm the theoretical results.}, journal={JOURNAL OF COMPUTATIONAL PHYSICS}, author={Zhang, Qian and Ito, Kazufumi and Li, Zhilin and Zhang, Zhiyue}, year={2015}, month={Oct}, pages={305–319} }
@article{ito_jin_takeuchi_2015, title={On the sectorial property of the Caputo derivative operator}, volume={47}, ISSN={["0893-9659"]}, DOI={10.1016/j.aml.2015.03.001}, abstractNote={In this note, we establish the sectorial property of the Caputo fractional derivative operator of order α∈(1,2) with a zero Dirichlet boundary condition.}, journal={APPLIED MATHEMATICS LETTERS}, author={Ito, Kazufumi and Jin, Bangti and Takeuchi, Tomoya}, year={2015}, month={Sep}, pages={43–46} }
@inproceedings{ito_landi_2015, title={The nonnegative matrix factorization and atomic deconvolution}, DOI={10.1109/bibm.2015.7359923}, abstractNote={The Nonnegative Matrix Factorization is an unsupervised maching learning technique that finds a representation of measured data in terms of two low-rank factors. It has recently gained popularity in various applications as a feature selection and dimension reduction tool, e.g. text mining, signal processing, and image processing. Thus, the nonnegative matrix factorization is an increasingly important tool in big data analysis as data continues to grow not only in size but also in complexity. In this paper, we advance the NMF analysis in the case of the convolution. That is, the two factors have the clear roles of convolution kernel and signal. Specifically, for the case of the point-spread function, atoms are the weights that describe the kernel. Using proper atoms, we develop a method for the blind deconvolution based on an NMF representation so that we obtain an estimate of the signal and the kernel. In addition, with Magnetic Resonance Imaging (MRI). Specifically, we extend the idea of the two factors to the Fourier transform and develop a coordinate-descent method in order to determine phases.}, booktitle={Proceedings 2015 ieee international conference on bioinformatics and biomedicine}, author={Ito, K. and Landi, A. K.}, year={2015}, pages={1650–1657} }
@article{ito_kunisch_2014, title={A Note on the Existence of Nonsmooth Nonconvex Optimization Problems}, volume={163}, ISSN={["1573-2878"]}, DOI={10.1007/s10957-014-0552-4}, abstractNote={Sufficient conditions for the existence of a solution to an abstract optimization problem in Banach spaces are given, which do not rely on convexity, regularity properties or a straightforward coerciveness assumption. Applications to sparsity-constrained optimization and to problems from mechanics are provided.}, number={3}, journal={JOURNAL OF OPTIMIZATION THEORY AND APPLICATIONS}, author={Ito, Kazufumi and Kunisch, Karl}, year={2014}, month={Dec}, pages={697–706} }
@article{chow_ito_zou_2014, title={A direct sampling method for electrical impedance tomography}, volume={30}, ISSN={["1361-6420"]}, DOI={10.1088/0266-5611/30/9/095003}, abstractNote={This work investigates the electrical impedance tomography (EIT) problem in the case when only one or two pairs of Cauchy data is available, which is known to be very difficult in achieving high reconstruction quality owing to its severely ill-posed nature. We propose a simple and efficient direct sampling method (DSM) to locate inhomogeneous inclusions. A new probing function based on the dipole potential is introduced to construct an indicator function for imaging the inclusions. Explicit formulae for the probing and indicator functions are derived in the case when the sampling domain is of spherical geometry in R n ?> (n = 2, 3). This new method is easy to implement and computationally cheap. Numerical experiments are presented to demonstrate the robustness and effectiveness of the DSM, which provides a new numerical approach for solving the EIT problem.}, number={9}, journal={INVERSE PROBLEMS}, author={Chow, Yat Tin and Ito, Kazufumi and Zou, Jun}, year={2014}, month={Sep} }
@article{ito_takeuchi_2014, title={Immersed Interface CIP for One Dimensional Hyperbolic Equations}, volume={16}, ISSN={["1991-7120"]}, DOI={10.4208/cicp.070313.221113a}, abstractNote={AbstractThe immersed interface technique is incorporated into CIP method to solve one-dimensional hyperbolic equations with piecewise constant coefficients. The proposed method achieves the third order of accuracy in time and space in the vicinity of the interface where the coefficients have jump discontinuities, which is the same order of accuracy of the standard CIP scheme. Some numerical tests are given to verify the accuracy of the proposed method.}, number={1}, journal={COMMUNICATIONS IN COMPUTATIONAL PHYSICS}, author={Ito, Kazufumi and Takeuchi, Tomoya}, year={2014}, month={Jul}, pages={96–114} }
@article{ito_jin_takeuchi_2014, title={Multi-parameter Tikhonov regularization - An augmented approach}, volume={35}, ISSN={["1860-6261"]}, DOI={10.1007/s11401-014-0835-y}, abstractNote={We study multi-parameter regularization (multiple penalties) for solving linear inverse problems to promote simultaneously distinct features of the sought-for objects. We revisit a balancing principle for choosing regularization parameters from the viewpoint of augmented Tikhonov regularization, and derive a new parameter choice strategy called the balanced discrepancy principle. A priori and a posteriori error estimates are provided to theoretically justify the principles, and numerical algorithms for efficiently implementing the principles are also provided. Numerical results on deblurring are presented to illustrate the feasibility of the balanced discrepancy principle.}, number={3}, journal={CHINESE ANNALS OF MATHEMATICS SERIES B}, author={Ito, Kazufumi and Jin, Bangti and Takeuchi, Tomoya}, year={2014}, month={May}, pages={383–398} }
@article{ito_kunisch_2014, title={OPTIMAL CONTROL WITH L-p(Omega), p epsilon [0,1), CONTROL COST}, volume={52}, ISSN={["1095-7138"]}, DOI={10.1137/120896529}, abstractNote={$L^p$ optimal control with $p\in [0,1)$ is investigated. The difficulty of natural lack of convexity and thus of weak lower semicontinuity is addressed by introducing appropriately chosen regularization terms. Existence results and necessary optimality conditions are obtained, and convergence of a monotone scheme is proved. Special attention is given to the particular case of optimal control problems with quadratic tracking and regularized $L^0$ control costs are given. A maximum principle is derived and existence of controls, in some cases relaxed controls, is proved, and an estimate on the consequences of relaxation are estimated.}, number={2}, journal={SIAM JOURNAL ON CONTROL AND OPTIMIZATION}, author={Ito, Kazufumi and Kunisch, Karl}, year={2014}, pages={1251–1275} }
@article{ito_jin_zou_2013, title={A direct sampling method for inverse electromagnetic medium scattering}, volume={29}, ISSN={["1361-6420"]}, DOI={10.1088/0266-5611/29/9/095018}, abstractNote={In this paper, we study the inverse electromagnetic medium scattering problem of estimating the support and shape of medium scatterers from scattered electric/magnetic near-field data. We shall develop a novel direct sampling method based on an analysis of electromagnetic scattering and the behavior of the fundamental solution. It is applicable to a few incident fields and needs only to compute inner products of the measured scattered field with the fundamental solutions located at sampling points. Hence, it is strictly direct, computationally very efficient and highly robust to the presence of data noise. Two- and three-dimensional numerical experiments indicate that it can provide reliable support estimates for multiple scatterers in the case of both exact and highly noisy data.}, number={9}, journal={INVERSE PROBLEMS}, author={Ito, Kazufumi and Jin, Bangti and Zou, Jun}, year={2013}, month={Sep} }
@article{ito_kunisch_2014, title={A variational approach to sparsity optimization based on Lagrange multiplier theory}, volume={30}, ISSN={["1361-6420"]}, DOI={10.1088/0266-5611/30/1/015001}, abstractNote={Sparsity optimization for linear least squares problems formulated as non-smooth regularization problems are considered in infinite-dimensional sequence spaces ℓp with p ∈ [0, 1]. Necessary optimality conditions in the format of a complementarity system are obtained. A monotonically convergent scheme is developed for the case p ∈ (0, 1]. For the case p = 0 a primal dual active set strategy based on the Lagrange multiplier rule is proposed and analyzed for special cases.}, number={1}, journal={INVERSE PROBLEMS}, author={Ito, Kazufumi and Kunisch, Karl}, year={2014}, month={Jan} }
@article{aihara_ito_nakagawa_takeuchi_2013, title={Optimal control laws for traffic flow}, volume={26}, ISSN={["0893-9659"]}, DOI={10.1016/j.aml.2012.12.021}, abstractNote={Optimal “on–off” laws for the traffic signals are developed based on the bilinear control problem with the binary constraints. A Lyapunov function based feedback law for regulating traffic congestions is developed. Also, a real-time optimal signal law is developed using a novel binary optimization method. Both methods are tested and compared, and our tests demonstrate that the both methods provide very effective and efficient traffic control laws.}, number={6}, journal={APPLIED MATHEMATICS LETTERS}, author={Aihara, K. and Ito, K. and Nakagawa, J. and Takeuchi, T.}, year={2013}, month={Jun}, pages={617–623} }
@article{ito_liu_2013, title={Recovery of inclusions in 2D and 3D domains for Poisson's equation}, volume={29}, ISSN={["1361-6420"]}, DOI={10.1088/0266-5611/29/7/075005}, abstractNote={In this paper, we consider the recovery problem of inclusions in three-dimensional and three-dimensional domains for Poisson’s equation from noisy observation data. We propose effective reconstruction algorithms to recover hidden inclusions within a body when one can only make measurements of voltage and current on the external boundary. Our motivation is to detect the number, the location, the size and the shape of inclusions. This problem is nonlinear and severely ill posed, thus we should apply regularization techniques in our approaches in order to improve the corresponding approximation. We give several examples to show the viability of our proposed methods.}, number={7}, journal={INVERSE PROBLEMS}, author={Ito, Kazufumi and Liu, Ji-Chuan}, year={2013}, month={Jul} }
@article{clason_ito_kunisch_2012, title={A MINIMUM EFFORT OPTIMAL CONTROL PROBLEM FOR ELLIPTIC PDES}, volume={46}, ISSN={["1290-3841"]}, DOI={10.1051/m2an/2011074}, abstractNote={This work is concerned with a class of minimum effort problems for partial differential equations, where the control cost is of L ∞ -type. Since this problem is non-differentiable, a regularized functional is introduced that can be minimized by a superlinearly convergent semi-smooth Newton method. Uniqueness and convergence for the solutions to the regularized problem are addressed, and a continuation strategy based on a model function is proposed. Numerical examples for a convection- diffusion equation illustrate the behavior of minimum effort controls. Mathematics Subject Classification. 49J52, 49J20, 49K20.}, number={4}, journal={ESAIM-MATHEMATICAL MODELLING AND NUMERICAL ANALYSIS-MODELISATION MATHEMATIQUE ET ANALYSE NUMERIQUE}, author={Clason, Christian and Ito, Kazufumi and Kunisch, Karl}, year={2012}, pages={911–927} }
@article{ito_jin_zou_2012, title={A direct sampling method to an inverse medium scattering problem}, volume={28}, ISSN={["1361-6420"]}, DOI={10.1088/0266-5611/28/2/025003}, abstractNote={In this work we present a novel sampling method for time harmonic inverse medium scattering problems. It provides a simple tool to directly estimate the shape of the unknown scatterers (inhomogeneous media), and it is applicable even when the measured data are only available for one or two incident directions. A mathematical derivation is provided for its validation. Two- and three-dimensional numerical simulations are presented, which show that the method is accurate even with a few sets of scattered field data, computationally efficient, and very robust with respect to noises in the data.}, number={2}, journal={INVERSE PROBLEMS}, author={Ito, Kazufumi and Jin, Bangti and Zou, Jun}, year={2012}, month={Feb} }
@article{ito_jin_zou_2013, title={A two-stage method for inverse medium scattering}, volume={237}, ISSN={["0021-9991"]}, DOI={10.1016/j.jcp.2012.12.004}, abstractNote={We present a novel numerical method to the time-harmonic inverse medium scattering problem of recovering the refractive index from near-field scattered data. The approach consists of two stages, one pruning step of detecting the scatterer support, and one resolution enhancing step with mixed regularization. The first step is strictly direct and of sampling type, and faithfully detects the scatterer support. The second step is an innovative application of nonsmooth mixed regularization, and it accurately resolves the scatterer sizes as well as intensities. The model is efficiently solved by a semi-smooth Newton-type method. Numerical results for two- and three-dimensional examples indicate that the approach is accurate, computationally efficient, and robust with respect to data noise.}, journal={JOURNAL OF COMPUTATIONAL PHYSICS}, author={Ito, Kazufumi and Jin, Bangti and Zou, Jun}, year={2013}, month={Mar}, pages={211–223} }
@article{ito_li_qiao_2012, title={The Sensitivity Analysis for the Flow Past Obstacles Problem with Respect to the Reynolds Number}, volume={4}, ISSN={["2070-0733"]}, DOI={10.4208/aamm.11-m1110}, abstractNote={AbstractIn this paper, numerical sensitivity analysis with respect to the Reynolds number for the flow past obstacle problem is presented. To carry out such analysis, at each time step, we need to solve the incompressible Navier-Stokes equations on irregular domains twice, one for the primary variables; the other is for the sensitivity variables with homogeneous boundary conditions. The Navier-Stokes solver is the augmented immersed interface method for Navier-Stokes equations on irregular domains. One of the most important contribution of this paper is that our analysis can predict the critical Reynolds number at which the vortex shading begins to develop in the wake of the obstacle. Some interesting experiments are shown to illustrate how the critical Reynolds number varies with different geometric settings.}, number={1}, journal={ADVANCES IN APPLIED MATHEMATICS AND MECHANICS}, author={Ito, Kazufumi and Li, Zhilin and Qiao, Zhonghua}, year={2012}, month={Feb}, pages={21–35} }
@article{ito_jin_takeuchi_2011, title={A REGULARIZATION PARAMETER FOR NONSMOOTH TIKHONOV REGULARIZATION}, volume={33}, ISSN={["1095-7197"]}, DOI={10.1137/100790756}, abstractNote={In this paper we develop a novel rule for choosing regularization parameters in nonsmooth Tikhonov functionals. It is solely based on the value function and applicable to a broad range of nonsmooth models, and it extends one known criterion. A posteriori error estimates of the approximations are derived. An efficient numerical algorithm for computing the minimizer is developed, and its convergence properties are discussed. Numerical results for several common nonsmooth models are presented, including deblurring natural images. The numerical results indicate the rule can yield results comparable with those achieved with the discrepancy principle and the optimal choice, and the algorithm merits a fast and steady convergence.}, number={3}, journal={SIAM JOURNAL ON SCIENTIFIC COMPUTING}, author={Ito, Kazufumi and Jin, Bangti and Takeuchi, Tomoya}, year={2011}, pages={1415–1438} }
@article{ito_jin_2011, title={A new approach to nonlinear constrained Tikhonov regularization}, volume={27}, ISSN={["1361-6420"]}, DOI={10.1088/0266-5611/27/10/105005}, abstractNote={We present a novel approach to nonlinear constrained Tikhonov regularization from the viewpoint of optimization theory. A second-order sufficient optimality condition is suggested as a nonlinearity condition to handle the nonlinearity of the forward operator. The approach is exploited to derive convergence rate results for a priori as well as a posteriori choice rules, e.g., discrepancy principle and balancing principle, for selecting the regularization parameter. The idea is further illustrated on a general class of parameter identification problems, for which (new) source and nonlinearity conditions are derived and the structural property of the nonlinearity term is revealed. A number of examples including identifying distributed parameters in elliptic differential equations are presented.}, number={10}, journal={INVERSE PROBLEMS}, author={Ito, Kazufumi and Jin, Bangti}, year={2011}, month={Oct} }
@article{ito_jin_zou_2011, title={A new choice rule for regularization parameters in Tikhonov regularization}, volume={90}, ISSN={["1563-504X"]}, DOI={10.1080/00036811.2010.541450}, abstractNote={This article proposes and analyses a novel heuristic rule for choosing regularization parameters in Tikhonov regularization for inverse problems. The existence of solutions to the regularization parameter equation is shown, and a variational characterization of the inverse solution is provided. Some a posteriori error estimates of the approximate solutions to the inverse problem are also established. An iterative algorithm is suggested for the efficient numerical realization of the new choice rule, which is shown to have a practically desirable monotone convergence. Numerical experiments for both mildly and severely ill-posed benchmark inverse problems with various regularizing functionals of Tikhonov type, e.g. L 2–L 2 with constraints, L 2–ℓ1 and L 1–TV, are presented to demonstrate its effectiveness, and compared with the quasi-optimality criterion.}, number={10}, journal={APPLICABLE ANALYSIS}, author={Ito, Kazufumi and Jin, Bangti and Zou, Jun}, year={2011}, pages={1521–1544} }
@article{banks_hu_ito_muccio_2011, title={Dynamic evasion-interrogation games with uncertainty in the context of electromagetics}, volume={4}, number={3}, journal={Numerical Mathematics: Theory, Methods and Applications}, author={Banks, H. T. and Hu, S. H. and Ito, K. and Muccio, S. G.}, year={2011}, pages={359–378} }
@article{ito_kunisch_2011, title={KARUSH-KUHN-TUCKER CONDITIONS FOR NONSMOOTH MATHEMATICAL PROGRAMMING PROBLEMS IN FUNCTION SPACES}, volume={49}, ISSN={["0363-0129"]}, DOI={10.1137/100817061}, abstractNote={Lagrange multiplier rules for abstract optimization problems with mixed smooth and convex terms in the cost, with smooth equality constrained and convex inequality constraints, are presented. The typical case for the equality constraints that the theory is meant for is given by differential equations. Applications are given to $L^1$-minimum norm control problems, $L^\infty$-norm minimization, and a class of optimal control problems with distributed state constraints and nonsmooth cost.}, number={5}, journal={SIAM JOURNAL ON CONTROL AND OPTIMIZATION}, author={Ito, Kazufumi and Kunisch, Karl}, year={2011}, pages={2133–2154} }
@article{ito_kunisch_2011, title={MINIMAL EFFORT PROBLEMS AND THEIR TREATMENT BY SEMISMOOTH NEWTON METHODS}, volume={49}, ISSN={["0363-0129"]}, DOI={10.1137/100784667}, abstractNote={The paper introduces minimum effort control problems. These provide an answer to the question of the smallest possible control bound which still allows us to drive the system to a target within a fixed time $T$. This is a counterpart to the time optimal control problem which minimizes the time required to drive the system to the target, given a control bound. The problem is formulated as an optimal control problem with pointwise constraint on the control. The necessary conditions of optimality are derived by Lagrange multiplier theory. The semismooth Newton method is applied to a properly regularized problem. Well-posedness and superlinear convergence of the semismooth Newton method are proved for linear control systems under a controllability condition. Numerical results are presented for demonstrating the applicability and feasibility of the proposed method.}, number={5}, journal={SIAM JOURNAL ON CONTROL AND OPTIMIZATION}, author={Ito, Kazufumi and Kunisch, Karl}, year={2011}, pages={2083–2100} }
@article{ito_kunisch_schulz_gherman_2010, title={APPROXIMATE NULLSPACE ITERATIONS FOR KKT SYSTEMS}, volume={31}, ISSN={["1095-7162"]}, DOI={10.1137/080724952}, abstractNote={We investigate a linear iteration scheme for solving Karush-Kuhn-Tucker systems arising from optimization problems with linear equality constraints. The iterations are motivated by the simplicity of the proposed combination of iterations for the forward and adjoint systems that need to be solved and for which efficient solvers may already be available. Convergence results are derived, and their practical relevance is investigated by means of a numerical example.}, number={4}, journal={SIAM JOURNAL ON MATRIX ANALYSIS AND APPLICATIONS}, author={Ito, Kazufumi and Kunisch, Karl and Schulz, Volker and Gherman, Ilia}, year={2010}, pages={1835–1847} }
@article{clason_ito_kunisch_2011, title={MINIMAL INVASION: AN OPTIMAL L-infinity STATE CONSTRAINT PROBLEM}, volume={45}, ISSN={["0764-583X"]}, DOI={10.1051/m2an/2010064}, abstractNote={In this work, the least pointwise upper and/or lower bounds on the state variable on a specified subdomain of a control system under piecewise constant control action are sought. This results in a non-smooth optimization problem in function spaces. Introducing a Moreau-Yosida regularization of the state constraints, the problem can be solved using a superlinearly convergent semi-smooth Newton method. Optimality conditions are derived, convergence of the Moreau-Yosida regularization is proved, and well-posedness and superlinear convergence of the Newton method is shown. Numerical examples illustrate the features of this problem and the proposed approach.}, number={3}, journal={ESAIM-MATHEMATICAL MODELLING AND NUMERICAL ANALYSIS-MODELISATION MATHEMATIQUE ET ANALYSE NUMERIQUE}, author={Clason, Christian and Ito, Kazufumi and Kunisch, Karl}, year={2011}, pages={505–522} }
@article{ito_kunisch_2010, title={SEMISMOOTH NEWTON METHODS FOR TIME-OPTIMAL CONTROL FOR A CLASS OF ODES}, volume={48}, ISSN={["1095-7138"]}, DOI={10.1137/090753905}, abstractNote={Time-optimal control problems for a class of linear multi-input systems are considered. The problems are regularized and the asymptotic and monotone behavior of the regularization procedure is investigated. For the regularized problems the applicability of semismooth Newton methods is verified. First numerical tests are presented which show that the proposed approach is different from other methods in that it does not rely on a priori information about the switching structure.}, number={6}, journal={SIAM JOURNAL ON CONTROL AND OPTIMIZATION}, author={Ito, Kazufumi and Kunisch, Karl}, year={2010}, pages={3997–4013} }
@article{ito_lai_li_2009, title={A well-conditioned augmented system for solving Navier-Stokes equations in irregular domains}, volume={228}, ISSN={["0021-9991"]}, DOI={10.1016/j.jcp.2008.12.028}, abstractNote={An augmented method based on a Cartesian grid is proposed for the incompressible Navier–Stokes equations in irregular domains. The irregular domain is embedded into a rectangular one so that a fast Poisson solver can be utilized in the projection method. Unlike several methods suggested in the literature that set the force strengths as unknowns, which often results in an ill-conditioned linear system, we set the jump in the normal derivative of the velocity as the augmented variable. The new approach improves the condition number of the system for the augmented variable significantly. Using the immersed interface method, we are able to achieve second order accuracy for the velocity. Numerical results and comparisons to benchmark tests are given to validate the new method. A lid-driven cavity flow with multiple obstacles and different geometries are also presented.}, number={7}, journal={JOURNAL OF COMPUTATIONAL PHYSICS}, author={Ito, Kazufumi and Lai, Ming-Chih and Li, Zhilin}, year={2009}, month={Apr}, pages={2616–2628} }
@article{ito_kunisch_2009, title={ASYMPTOTIC PROPERTIES OF FEEDBACK SOLUTIONS FOR A CLASS OF QUANTUM CONTROL PROBLEMS}, volume={48}, ISSN={["1095-7138"]}, DOI={10.1137/080720784}, abstractNote={Control of quantum systems described by the Schrodinger equation is considered. Feedback control laws are developed for orbit tracking via controlled Hamiltonians, and their asymptotic properties are analyzed. Numerical integration via time splitting is also investigated and used to demonstrate the feasibility of the proposed feedback laws.}, number={4}, journal={SIAM JOURNAL ON CONTROL AND OPTIMIZATION}, author={Ito, Kazufumi and Kunisch, Karl}, year={2009}, pages={2323–2343} }
@article{ito_toivanen_2009, title={LAGRANGE MULTIPLIER APPROACH WITH OPTIMIZED FINITE DIFFERENCE STENCILS FOR PRICING AMERICAN OPTIONS UNDER STOCHASTIC VOLATILITY}, volume={31}, ISSN={["1095-7197"]}, DOI={10.1137/07070574X}, abstractNote={The deterministic numerical valuation of American options under Heston's stochastic volatility model is considered. The prices are given by a linear complementarity problem with a two- dimensional parabolic partial differential operator. A new truncation of the domain is described for small asset values, while for large asset values and variance a standard truncation is used. The finite difference discretization is constructed by numerically solving a quadratic optimization problem aiming to minimize the truncation error at each grid point. A Lagrange approach is used to treat the linear complementarity problems. Numerical examples demonstrate the accuracy and effectiveness of the proposed approach.}, number={4}, journal={SIAM JOURNAL ON SCIENTIFIC COMPUTING}, author={Ito, Kazufumi and Toivanen, Jari}, year={2009}, pages={2646–2664} }
@article{haslinger_ito_kozubek_kunisch_peichl_2009, title={On the shape derivative for problems of Bernoulli type}, volume={11}, DOI={10.4171/ifb/213}, abstractNote={The shape derivative of the cost functional in a Bernoulli-type problem is characterized. The calculation of the derivative of the cost does not use the shape derivative of the state variable and is achieved under mild regularity conditions on the boundary of the domain.}, number={2}, journal={Interfaces and Free Boundaries}, author={Haslinger, J. and Ito, K. and Kozubek, T. and Kunisch, K. and Peichl, G.}, year={2009}, pages={317–330} }
@article{ito_kunisch_2010, title={Optimal control of parabolic variational inequalities}, volume={93}, ISSN={["0021-7824"]}, DOI={10.1016/j.matpur.2009.10.005}, abstractNote={Optimal control of parabolic variational inequalities is studied in the case where the spatial domain is not necessarily bounded. First, strong and weak solutions concepts for the variational inequality are proposed and existence results are obtained by a monotone and a finite difference technique. An optimal control problem with the control appearing in the coefficient of the leading term is investigated and a first order optimality system in a Lagrangian framework is derived. On étudie le contrôle optimal d'inégalités variationnelles dans le cas où le domaine spatial n'est pas nécessairement borné. Tout d'abord, on introduit des concepts de solutions fortes et faibles pour l'inégalité variationnelle et on obtient des résultats d'existence par une méthode de différences finies et monotone. On examine ensuite un problème de contrôle optimal avec un contrôle apparaissant dans le coefficient du terme principal et on en déduit un système d'optimalité du premier ordre dans un cadre lagrangien.}, number={4}, journal={JOURNAL DE MATHEMATIQUES PURES ET APPLIQUEES}, author={Ito, Kazufumi and Kunisch, Karl}, year={2010}, month={Apr}, pages={329–360} }
@article{ito_qiao_toivanen_2008, title={A domain decomposition solver for acoustic scattering by elastic objects in layered media}, volume={227}, ISSN={["1090-2716"]}, DOI={10.1016/j.jcp.2008.06.015}, abstractNote={A finite element solution procedure is presented for accurately computing time-harmonic acoustic scattering by elastic targets buried in sediment. An improved finite element discretization based on trilinear basis functions leading to fourth-order phase accuracy is described. For sufficiently accurate discretizations 100 million to 1 billion unknowns are required. The resulting systems of linear equations are solved iteratively using the GMRES method with a domain decomposition preconditioner employing a fast direct solver. Due to the construction of the discretization and preconditioner, iterations can be reduced onto a sparse subspace associated with the interfaces. Numerical experiments demonstrate capability to evaluate the scattered field with hundreds of wavelengths.}, number={19}, journal={JOURNAL OF COMPUTATIONAL PHYSICS}, author={Ito, Kazufumi and Qiao, Zhonghua and Toivanen, Jari}, year={2008}, month={Oct}, pages={8685–8698} }
@inproceedings{xie_ito_li_toivanen_2008, title={A finite element method for interface problems with locally modified triangulations}, volume={466}, DOI={10.1090/conm/466/09122}, booktitle={Moving interface problems and applications in fluid dynamics}, author={Xie, H. and Ito, K. and Li, Zhilin and Toivanen, J.}, year={2008}, pages={179–190} }
@article{ito_qiao_2008, title={A high order compact MAC finite difference scheme for the Stokes equations: Augmented variable approach}, volume={227}, ISSN={0021-9991}, url={http://dx.doi.org/10.1016/j.jcp.2008.05.021}, DOI={10.1016/j.jcp.2008.05.021}, abstractNote={This paper deals with the steady Stokes flow on a rectangular domain. A high order compact MAC finite difference scheme based on the staggered grid is developed for solving Stokes equations with a Dirichlet boundary condition on the velocity. A novel high order boundary treatment is developed via introducing a suitable augmented variable. The accuracy of the proposed method is demonstrated in test problems. Creeping flow solutions for driven cavity problem are obtained numerically and compared with published results.}, number={17}, journal={Journal of Computational Physics}, publisher={Elsevier BV}, author={Ito, Kazufumi and Qiao, Zhonghua}, year={2008}, month={Sep}, pages={8177–8190} }
@inproceedings{ito_qiao_2008, title={A high order finite difference scheme for the Stokes equations}, volume={466}, DOI={10.1090/conm/466/09115}, booktitle={Moving interface problems and applications in fluid dynamics}, author={Ito, K. and Qiao, Z.}, year={2008}, pages={35–51} }
@article{demetriou_ito_smith_2009, title={Adaptive techniques for the MRAC, adaptive parameter identification, and on-line fault monitoring and accommodation for a class of positive real infinite dimensional systems}, volume={23}, ISSN={["1099-1115"]}, DOI={10.1002/acs.1058}, abstractNote={AbstractA theoretical framework of the model reference adaptive control design, adaptive parameter identification and automated fault detection is developed for a class of positive real infinite dimensional systems. Uncertain terms are treated as additive perturbations of the plant operator and the framework provides a unified treatment for model reference control, parameter estimation and fault detection and accommodation. For each design problem the well‐posedness and stability of the proposed adaptive scheme are investigated. Extensions to the variable structure observer, to specific forms of the structured perturbation terms and to slowly time‐varying systems are also considered within the proposed framework. Such results are summarized as they capitalize on the proposed well‐posedness and stability results for the general cases. Copyright © 2008 John Wiley & Sons, Ltd.}, number={2}, journal={INTERNATIONAL JOURNAL OF ADAPTIVE CONTROL AND SIGNAL PROCESSING}, author={Demetriou, Michael A. and Ito, Kazufumi and Smith, Ralph C.}, year={2009}, month={Feb}, pages={193–215} }
@article{ito_kunisch_2008, title={REDUCED-ORDER OPTIMAL CONTROL BASED ON APPROXIMATE INERTIAL MANIFOLDS FOR NONLINEAR DYNAMICAL SYSTEMS}, volume={46}, ISSN={["1095-7170"]}, DOI={10.1137/060666421}, abstractNote={A reduced-order method for optimal control problems in infinite dimensions based on approximate inertial manifolds is developed. Convergence of the cost, optimal controls, and optimal states of the finite dimensional, reduced-order, optimal control problems to the original optimal control problem is analyzed. Special attention is given to the particular case when the dynamics are described by the Navier-Stokes equations in dimension two.}, number={6}, journal={SIAM JOURNAL ON NUMERICAL ANALYSIS}, author={Ito, Kazufumi and Kunisch, Karl}, year={2008}, pages={2867–2891} }
@article{ito_kunisch_2008, title={Semi-smooth Newton methods for the Signorini problem}, volume={53}, ISSN={["0862-7940"]}, DOI={10.1007/s10492-008-0036-7}, abstractNote={Semi-smooth Newton methods are analyzed for the Signorini problem. A proper regularization is introduced which guarantees that the semi-smooth Newton method is superlinearly convergent for each regularized problem. Utilizing a shift motivated by an augmented Lagrangian framework, to the regularization term, the solution to each regularized problem is feasible. Convergence of the regularized problems is shown and a report on numerical experiments is given.}, number={5}, journal={APPLICATIONS OF MATHEMATICS}, author={Ito, Kazufumi and Kunisch, Karl}, year={2008}, month={Oct}, pages={455–468} }
@article{ito_kunisch_peichl_2008, title={Variational approach to shape derivatives}, volume={14}, ISSN={["1292-8119"]}, DOI={10.1051/cocv:2008002}, abstractNote={A general framework for calculating shape derivatives for optimization problems with partial differential equations as constraints is presented. The proposed technique allows to obtain the shape derivative of the cost without the necessity to involve the shape derivative of the state variable. In fact, the state variable is only required to be Lipschitz continuous with respect to the geometry perturbations. Applications to inverse interface problems, and shape optimization for elliptic systems and the Navier-Stokes equations are given.}, number={3}, journal={ESAIM-CONTROL OPTIMISATION AND CALCULUS OF VARIATIONS}, author={Ito, Kazufumi and Kunisch, Karl and Peichl, Gunther H.}, year={2008}, pages={517–539} }
@article{demetriou_ito_smith_2007, title={Adaptive monitoring and accommodation of nonlinear actuator faults in positive real infinite dimensional systems}, volume={52}, ISSN={["1558-2523"]}, DOI={10.1109/TAC.2007.910694}, abstractNote={We consider a class of positive real infinite dimensional systems which are subjected to incipient actuator faults. The actuator fault is modeled as a time varying transition from an initial (linear or nonlinear) map into another unknown nonlinear map at the onset of the fault occurrence. An infinite dimensional adaptive detection observer is utilized to generate a residual signal in order to detect the fault occurrence and to assist in the fault accommodation. This is done via an automated control reconfiguration which utilizes information on the new actuator map and adjusts the controller via a right inverse of the actuator map. A robust modification is utilized in order to avoid false alarms caused by unmodelled dynamics. An example is included to illustrate the applicability of the proposed scheme}, number={12}, journal={IEEE TRANSACTIONS ON AUTOMATIC CONTROL}, author={Demetriou, Michael A. and Ito, Kazufumi and Smith, Ralph C.}, year={2007}, month={Dec}, pages={2332–2338} }
@article{li_lai_ito_2007, title={An immersed interface method for the Navier-Stokes equations on irregular domains}, volume={7}, ISSN={1617-7061 1617-7061}, url={http://dx.doi.org/10.1002/pamm.200700758}, DOI={10.1002/pamm.200700758}, abstractNote={AbstractAn augmented method based on a Cartesian grid is proposed for the incompressible Navier Stokes equations on an irregular domain. The irregular domain is embedded into a rectangular one so that a fast Poisson solver can be used in the projection method. Unlike several methods suggested in the literature that set the force strengths as unknowns, which often results an ill‐conditioned linear system, we set the jump in the normal derivative of the velocity as the augmented variable. The new approach improve the condition number of the system for the augmented variable significantly. Using the immersed interface method, we achieve second order accuracy for the velocity. Numerical results and comparisons are given to validate the new method. Some interesting new numerical experiments results are also presented. (© 2008 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)}, number={1}, journal={PAMM}, publisher={Wiley}, author={Li, Zhilin and Lai, Ming-Chih and Ito, Kazufumi}, year={2007}, month={Dec}, pages={1025401–1025402} }
@article{ito_kunisch_2007, title={Convergence of the primal-dual active set strategy for diagonally dominant systems}, volume={46}, ISSN={["0363-0129"]}, DOI={10.1137/050632713}, abstractNote={Sufficient conditions for global convergence of the primal-dual active set strategy for finite and infinite dimensional quadratic, as well as nonlinear optimization, problems with affine equality and inequality constraints are presented. These conditions involve diagonal dominance and cone preserving properties of the operator defining the cost functional. Globalization strategies are also provided, and specific sufficient conditions for the primal-dual active set step to have a descent property are given.}, number={1}, journal={SIAM JOURNAL ON CONTROL AND OPTIMIZATION}, author={Ito, Kazufumi and Kunisch, Karl}, year={2007}, pages={14–34} }
@article{ito_kunisch_2009, title={On a semi-smooth Newton method and its globalization}, volume={118}, ISSN={["1436-4646"]}, DOI={10.1007/s10107-007-0196-3}, abstractNote={This paper addresses the globalization of the semi-smooth Newton method for non-smooth equations F(x) = 0 in $${\mathbb{R}}^m$$ with applications to complementarity and discretized ℓ1-regularization problems. Assuming semi-smoothness it is shown that super-linearly convergent Newton methods can be globalized, if appropriate descent directions are used for the merit function |F(x)|2. Special attention is paid to directions obtained from the primal-dual active set strategy.}, number={2}, journal={MATHEMATICAL PROGRAMMING}, author={Ito, Kazufumi and Kunisch, Karl}, year={2009}, month={May}, pages={347–370} }
@article{ito_kunisch_2007, title={Optimal bilinear control of an abstract Schrodinger equation}, volume={46}, ISSN={["0363-0129"]}, DOI={10.1137/05064254X}, abstractNote={Well-posedness of abstract quantum mechanical systems is considered and the existence of optimal control of such systems is proved. First order optimality systems are derived. Convergence of the monotone scheme for the solution of the optimality system is proved.}, number={1}, journal={SIAM JOURNAL ON CONTROL AND OPTIMIZATION}, author={Ito, Kazufumi and Kunisch, Karl}, year={2007}, pages={274–287} }
@article{ito_kunisch_2007, title={Optimal control of obstacle problems by H-1-obstacles}, volume={56}, ISSN={["1432-0606"]}, DOI={10.1007/s00245-007-0877-6}, number={1}, journal={APPLIED MATHEMATICS AND OPTIMIZATION}, author={Ito, Kazufumi and Kunisch, Karl}, year={2007}, pages={1–17} }
@article{ito_kunisch_peichl_2007, title={Shape derivatives without taking the shape derivative}, volume={7}, ISSN={1617-7061 1617-7061}, url={http://dx.doi.org/10.1002/pamm.200700780}, DOI={10.1002/pamm.200700780}, abstractNote={AbstractA general framework for calculating shape derivatives for optimization problems with partial differential equations as constraints is presented. Exploiting the structure of the cost functional the proposed technique allows to obtain the shape derivative of the cost without the necessity to involve the shape derivative of the state variable. (© 2008 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)}, number={1}, journal={PAMM}, publisher={Wiley}, author={Ito, K. and Kunisch, K. and Peichl, G.}, year={2007}, month={Dec}, pages={1061005–1061006} }
@article{ito_toivanen_2007, title={A fast iterative solver for scattering by elastic objects in layered media}, volume={57}, ISSN={["1873-5460"]}, DOI={10.1016/j.apnum.2006.07.020}, abstractNote={We developed a fast iterative solver for computing time-harmonic acoustic waves scattered by an elastic object in layered media. The discretization of the problem was performed using a finite element method with linear elements based on a locally body-fitted uniform triangulation. We used a domain decomposition preconditioner in the iterative solution of the resulting system of linear equations. The preconditioner was based on a cyclic reduction type fast direct solver. The solution procedure reduces GMRES iterates onto a sparse subspace which decreases the storage and computational requirements essentially. The numerical results demonstrate the effectiveness of the proposed approach for two-dimensional domains that are hundreds of wavelengths wide and require the solution of linear systems with several millions of unknowns.}, number={5-7}, journal={APPLIED NUMERICAL MATHEMATICS}, author={Ito, K. and Toivanen, J.}, year={2007}, pages={811–820} }
@article{ackleh_deng_ito_thibodeaux_2006, title={A structured erythropoiesis model with nonlinear cell maturation velocity and hormone decay rate}, volume={204}, ISSN={["1879-3134"]}, DOI={10.1016/j.mbs.2006.08.004}, abstractNote={We develop a quasilinear structured model that describes the regulation of erythropoiesis, the process in which red blood cells are developed. In our model, the maturation velocity of precursor cells is assumed to be a function of the erythropoietin hormone, and the decay rate of this hormone is assumed to be a function of the number of precursor cells, unlike other models which assume these parameters to be constants. Existence-uniqueness results are established and convergence of a finite difference approximation to the unique solution of the model is obtained. The finite difference scheme is then used to investigate the effects of these nonlinear parameters on the model dynamics. Our results show that a velocity of precursor cells maturation rate which is an increasing function of the hormone level and a decay rate of the hormone which is an increasing function of the number of precursor cells have a stabilizing effect on the dynamics of the model. While assuming that one parameter is a function and letting the other be a constant stabilizes the oscillations in the mature cells level, the effect is more significant when both parameters are taken to be functions. A study of robustness with respect to the forms of these functions and parameter sensitivity is also carried out.}, number={1}, journal={MATHEMATICAL BIOSCIENCES}, author={Ackleh, Azmy S. and Deng, Keng and Ito, Kazufumi and Thibodeaux, Jeremy}, year={2006}, month={Nov}, pages={21–48} }
@article{li_ito_lai_2007, title={An augmented approach for Stokes equations with a discontinuous viscosity and singular forces}, volume={36}, ISSN={["1879-0747"]}, DOI={10.1016/j.compfluid.2006.03.003}, abstractNote={For Stokes equations with a discontinuous viscosity across an arbitrary interface or/and singular forces along the interface, it is known that the pressure is discontinuous and the velocity is non-smooth. It has been shown that these discontinuities are coupled together, which makes it difficult to obtain accurate numerical solutions. In this paper, a new numerical method that decouples the jump conditions of the fluid variables through two augmented variables has been developed. The GMRES iterative method is used to solve the Schur complement system for the augmented variables that are only defined on the interface. The augmented approach also rescales the Stokes equations in such a way that a fast Poisson solver can be used in each iteration. Numerical tests using examples that have analytic solutions show that the new method has average second order accuracy for the velocity in the infinity norm. An example of a moving interface problem is also presented.}, number={3}, journal={COMPUTERS & FLUIDS}, author={Li, Zhilin and Ito, Kazufumi and Lai, Ming-Chih}, year={2007}, month={Mar}, pages={622–635} }
@article{li_wan_ito_lubkin_2006, title={An augmented approach for the pressure boundary condition in a Stokes flow}, volume={1}, number={5}, journal={Communications in Computational Physics}, author={Li, Z. L. and Wan, X. H. and Ito, K. and Lubkin, S. R.}, year={2006}, pages={874–885} }
@article{banks_ito_toivanen_2006, title={Determination of interrogating frequencies to maximize electromagnetic backscatter from objects with material coatings}, volume={1}, number={2}, journal={Communications in Computational Physics}, author={Banks, H. T. and Ito, K. and Toivanen, J.}, year={2006}, pages={362–382} }
@article{banks_ito_kepler_toivanen_2006, title={Material surface design to counter electromagnetic interrogation of targets}, volume={66}, ISSN={["1095-712X"]}, DOI={10.1137/040621430}, abstractNote={Utilization of controllable ferromagnetic layers coating a conducting object to provide an attenuation capability against electromagnetic interrogation is discussed. The problem is formulated as a differential game and/or a robust optimization. The scattered field due to interrogation can be attenuated with the assumption of an uncertainty in the interrogation wave numbers. The controllable layer composed of ferromagnetic materials [H. How and C. Vittoria, Implementation of Microwave Active Nulling, private communication; H. How and C. Vittoria, IEEE Trans. Microwave Theory Tech., 52 (2004), pp. 2177-2182] is incorporated in a mathematical formulation based on the time-harmonic Maxwell equation. Fresnel's law for the reflectance index is extended to the electromagnetic propagation in anisotropic composite layers of ferromagnetic and electronic devices and is used to demonstrate feasibility of control of reflections. Our methodology is also tested for a nonplanar geometry of the conducting object (an NACA ...}, number={3}, journal={SIAM JOURNAL ON APPLIED MATHEMATICS}, author={Banks, HT and Ito, K and Kepler, GM and Toivanen, JA}, year={2006}, pages={1027–1049} }
@article{ito_toivanen_2006, title={Preconditioned iterative methods on sparse subspaces}, volume={19}, ISSN={["0893-9659"]}, DOI={10.1016/j.aml.2005.11.027}, abstractNote={When some rows of the system matrix and a preconditioner coincide, preconditioned iterations can be reduced to a sparse subspace. Taking advantage of this property can lead to considerable memory and computational savings. This is particularly useful with the GMRES method. We consider the iterative solution of a discretized partial differential equation on this sparse subspace. With a domain decomposition method and a fictitious domain method the subspace corresponds a small neighborhood of an interface. As numerical examples we solve the Helmholtz equation using a fictitious domain method and an elliptic equation with a jump in the diffusion coefficient using a separable preconditioner.}, number={11}, journal={APPLIED MATHEMATICS LETTERS}, author={Ito, Kazufumi and Toivanen, Jari}, year={2006}, month={Nov}, pages={1191–1197} }
@article{ito_kunisch_2006, title={Receding horizon control with incomplete observations}, volume={45}, ISSN={["1095-7138"]}, DOI={10.1137/S0363012903437988}, abstractNote={To overcome the difficulties related to the computational requirements for solving the optimality systems for optimal control problems on long time horizons, receding horizon techniques provide an important alternative. Rather than finding the optimal solution, a suboptimal control is obtained which achieves the design objective with significantly less computational effort. Moreover, the obtained control can be interpreted as a state feedback control. In this work we continue our analysis of receding horizon strategies, considering the situation when only partial state observations are available. The receding horizon strategy is combined with a state estimator framework. A linear quadratic Gaussian design based on a linearization procedure is proposed and its asymptotic performance is analyzed for systems with nonlinear dynamics. Numerical examples validate the proposed methodology.}, number={1}, journal={SIAM JOURNAL ON CONTROL AND OPTIMIZATION}, author={Ito, K and Kunisch, K}, year={2006}, pages={207–225} }
@book{li_ito_2006, title={The immersed interface method: Numerical solutions of PDEs involving interfaces and irregular domains}, ISBN={0898716098}, DOI={10.1137/1.9780898717464}, publisher={Philadelphia: SIAM, Society for Industrial and Applied Mathematics}, author={Li, Zhilin and Ito, K.}, year={2006} }
@article{fang_ito_redfern_2006, title={A homogenization model for laser beam-induced current imaging and detection of non-uniformities in semiconductor arrays}, volume={194}, ISSN={["1879-1778"]}, DOI={10.1016/j.cam.2005.08.007}, abstractNote={We present an approximate model for laser beam-induced current (LBIC) imaging of arrays of semiconductor devices based on homogenization. LBIC is a non-destructive technique useful for the characterization and quality control of semiconductor focal plane arrays, a key component in modern imaging systems. The model provides not only an efficient alternative for LBIC image simulation of large uniform arrays, but also an effective method for detection of non-uniformities among arrays. Numerical examples are presented to illustrate the effectiveness of this method in detecting array non-uniformities due to variations in dislocation/size or doping level among p–n junction diodes.}, number={2}, journal={JOURNAL OF COMPUTATIONAL AND APPLIED MATHEMATICS}, author={Fang, Weifu and Ito, Kazufumi and Redfern, David A.}, year={2006}, month={Oct}, pages={395–408} }
@article{hicks_ito_2005, title={A method for determination of optimal gaits with application to a snake-like serial-link structure}, volume={50}, ISSN={["1558-2523"]}, DOI={10.1109/tac.2005.854583}, abstractNote={In this paper, we present a method of determining optimal gaits for shape actuated locomotion systems. This method is the synthesis of techniques for computing reduced equations for robotic locomotion systems and a numerical optimal control strategy. Symmetry reduction processes induce a form of locomotion system dynamics that reveals a cyclic-like coupling between group, shape, and momenta coordinates. This form allows one to focus on designing gaits, abandoning concern over shape dynamics. Using this vantage point we indicate how a numerical optimal control method based on Gaussian quadrature may be acclimatized to periodicity, thus providing optimal gaits. The method is demonstrated by means of its application to a snake-like serial-link structure or snake robot. This application provides scientific merit to hypotheses concerning observed locomotion phenomena amongst animals employing undulatory propulsive mechanisms.}, number={9}, journal={IEEE TRANSACTIONS ON AUTOMATIC CONTROL}, author={Hicks, G and Ito, K}, year={2005}, month={Sep}, pages={1291–1306} }
@article{ito_2005, title={An optimal optical flow}, volume={44}, ISSN={["0363-0129"]}, DOI={10.1137/S0363012904433444}, abstractNote={The problem of determining optical flow for the image registration problem is discussed. Feedback solutions are proposed, and it is shown that they are optimal for certain optimal control formulations of the problem. Well-posedness of the proposed feedback solutions is analyzed, and numerical findings are presented.}, number={2}, journal={SIAM JOURNAL ON CONTROL AND OPTIMIZATION}, author={Ito, K}, year={2005}, pages={728–742} }
@article{ito_li_kyei_2005, title={Higher-order, Cartesian grid based finite difference schemes for elliptic equations on irregular domains}, volume={27}, ISSN={["1095-7197"]}, DOI={10.1137/03060120X}, abstractNote={Second and fourth order Cartesian grid based finite difference methods are proposed for elliptic and parabolic partial differential equations, and associated eigenvalue problems on irregular domains with general boundary conditions. Our methods are based on the continuation of a solution idea using multivariable Taylor's expansion of the solution about selected boundary points, and the core ideas of the immersed interface method. The methods offer systematic treatment of the general boundary conditions in two- and three-dimensional domains and are directly applied to semi-discretize heat equations on irregular domains. Convergence analysis and numerical examples are presented. The validity and effectiveness of the proposed methods are demonstrated through our numerical results including computations of the eigenvalues of the associated eigenvalue problem.}, number={1}, journal={SIAM JOURNAL ON SCIENTIFIC COMPUTING}, author={Ito, K and Li, ZL and Kyei, Y}, year={2005}, pages={346–367} }
@article{ito_li_2006, title={Interface conditions for Stokes equations with a discontinuous viscosity and surface sources}, volume={19}, ISSN={["0893-9659"]}, DOI={10.1016/j.aml.2005.02.041}, abstractNote={The interface conditions, or jump conditions, for the pressure and the velocity of the solution to the incompressible Stokes equations with a discontinuous viscosity and a singular source along an interface are derived in this work. While parts of the results agree with those in the literature, some of the results are new. These theoretical results are useful for developing accurate numerical methods for the interface problem.}, number={3}, journal={APPLIED MATHEMATICS LETTERS}, author={Ito, K and Li, ZL}, year={2006}, month={Mar}, pages={229–234} }
@article{redfern_fang_ito_bahir_musca_dell_faraone_2005, title={Investigation of laser beam-induced current techniques for heterojunction photodiode characterization}, volume={98}, ISSN={["1089-7550"]}, DOI={10.1063/1.1993754}, abstractNote={A reduced model is developed that has significant advantages over the full drift-diffusion model for the simulation of laser beam-induced current (LBIC) signals in the presence of heterojunctions. The model determines the contribution to the LBIC signal that would occur from photogeneration at any position within the semiconductor, and is particularly useful for heterostructures where judicious choice of illumination wavelength can result in photogeneration at different depths within the device structure. The reduced model is used to examine the basic features of LBIC as applied to two types of planar P-n HgCdTe heterojunction photodiode structures. In particular, the question of correctly identifying erroneous device structures formed during the fabrication process is addressed, and experimental measurements are presented to support the simulation results.}, number={3}, journal={JOURNAL OF APPLIED PHYSICS}, author={Redfern, DA and Fang, W and Ito, K and Bahir, G and Musca, CA and Dell, JM and Faraone, L}, year={2005}, month={Aug} }
@article{ackleh_ito_2005, title={Measure-valued solutions for a hierarchically size-structured population}, volume={217}, ISSN={["0022-0396"]}, DOI={10.1016/j.jde.2004.12.013}, abstractNote={We present a hierarchically size-structured population model with growth, mortality and reproduction rates which depend on a function of the population density (environment). We present an example to show that if the growth rate is not always a decreasing function of the environment (e.g., a growth which exhibits the Allee effect) the emergence of a singular solution which contains a Dirac delta mass component is possible, even if the vital rates of the individual and the initial data are smooth functions. Therefore, we study the existence of measure-valued solutions. Our approach is based on the vanishing viscosity method.}, number={2}, journal={JOURNAL OF DIFFERENTIAL EQUATIONS}, author={Ackleh, AS and Ito, K}, year={2005}, month={Oct}, pages={431–455} }
@article{ito_kunisch_2006, title={Parabolic variational inequalities: The Lagrange multiplier approach}, volume={85}, ISSN={["1776-3371"]}, DOI={10.1016/j.matpur.2005.08.005}, abstractNote={Parabolic variational inequalities are discussed and existence and uniqueness of strong as well as weak solutions are established. Our approach is based on a Lagrange multiplier treatment. Existence is obtained as the unique asymptotic limit of solutions to a family of appropriately regularized nonlinear parabolic equations. Two regularization techniques are presented resulting in feasible and unfeasible approximations respectively. Monotonicity results of the regularized solutions and convergence rate estimate are established. The results are applied to the Black–Scholes model for American options. The case of the bilateral constraints is also treated. Numerical results for the Black–Scholes model are presented and prove the practical efficiency of our results. Des inégalités variationnelles paraboliques sont discutées et l'existence et l'unicité des solutions fortes faibles sont établies. Notre approche des solutions utilise une méthode de multiplicateur de Lagrange. L'existence est obtenue comme limite asymptotique unique des solutions à une famille d'équations paraboliques non linéaires convenablement régularisées. Deux techniques de régularisation sont présentées ayant pour résultat des approximations acceptées ou rejetées. Des résultats de monotonie des solutions régularisées et d'évaluation de taux de convergence sont établis. Les résultats sont appliqués au modèle Black–Scholes pour des options américaines. Le cas des contraintes bilatérales est également traité. Des résultats numériques pour le modèle Black–Scholes sont présentés et prouvent l'efficacité pratique de nos techniques.}, number={3}, journal={JOURNAL DE MATHEMATIQUES PURES ET APPLIQUEES}, author={Ito, K and Kunisch, K}, year={2006}, month={Mar}, pages={415–449} }
@article{ito_kunisch_peichl_2006, title={Variational approach to shape derivatives for a class of Bernoulli problems}, volume={314}, ISSN={["1096-0813"]}, DOI={10.1016/j.jmaa.2005.03.100}, abstractNote={The shape derivative of a functional related to a Bernoulli problem is derived without using the shape derivative of the state. The gradient information is combined with level set ideas in a steepest descent algorithm. Numerical examples show the feasibility of the approach.}, number={1}, journal={JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS}, author={Ito, K and Kunisch, K and Peichl, GH}, year={2006}, month={Feb}, pages={126–149} }
@article{fang_ito_redfern_2004, title={LBIC imaging of semiconductor arrays: The cross-sectional model}, volume={40}, ISSN={["1872-9479"]}, DOI={10.1016/j.mcm.2003.10.045}, abstractNote={Laser beam induced current (LBIC)/nondestructive technique that has been used for a number of years to qualitatively examine large arrays of p-n junctions, especially in HgCdTe infrared focal plane arrays. In this paper, we quantitatively study the application of the LBIC imaging technique to semiconductor arrays Based on a previous mathematical model for LBIC applied to individual devices, we employ the homogenization method to derive approximations of the LBIC images of large arrays. Such approximations reduce the computational burden in simulations of these LBIC bouges. We then illustrate the application of our approximations for the purpose of recovering array parameters from the LBIC images.}, number={1-2}, journal={MATHEMATICAL AND COMPUTER MODELLING}, author={Fang, WF and Ito, K and Redfern, DA}, year={2004}, month={Jul}, pages={127–136} }
@article{kojima_ito_2004, title={Reconstruction of magnetic charge densities using regularization of bounded variations under noisy observations}, volume={19}, ISSN={["1383-5416"]}, DOI={10.3233/jae-2004-582}, abstractNote={This paper is concerned with computational and regularization techniques for recovering induced magnetic fields due to the existence of cracks. The problem is formulated as an inverse problem with a set of source functions of the distribution type. The regularization of bounded variation is effectively used for solving the severe ill-posed problem. A iterative solver is proposed by a integro-differential equation with time marching scheme. For the practical implementation of the numerical treatment, a finite difference scheme is adopted to the proposed method with the aid of discrete fast Fourier transform. Some successful numerical experiments are demonstrated for the validity of the proposed method.}, number={1-4}, journal={INTERNATIONAL JOURNAL OF APPLIED ELECTROMAGNETICS AND MECHANICS}, author={Kojima, F and Ito, K}, year={2004}, pages={309–313} }
@article{ito_kunisch_2006, title={Reduced order control based on approximate inertial manifolds}, volume={415}, ISSN={["1873-1856"]}, DOI={10.1016/j.laa.2004.10.019}, abstractNote={A reduced-order method based on approximate inertial manifolds is applied to optimal control problems in infinite-dimensional state spaces. A detailed analysis of the method is given for the linear quadratic regulator problem. The method can also be applied to higher-order control systems with an appropriate decomposition of the state space in terms of slow and fast exponential decay.}, number={2-3}, journal={LINEAR ALGEBRA AND ITS APPLICATIONS}, author={Ito, Kazufumi and Kunisch, Karl}, year={2006}, month={Jun}, pages={531–541} }
@article{ito_kunisch_2004, title={The primal-dual active set method for nonlinear optimal control problems with bilateral constraints}, volume={43}, ISSN={["1095-7138"]}, DOI={10.1137/S0363012902411015}, abstractNote={The primal-dual active set method has proved to be an efficient numerical tool in the context of diverse applications. So far it has been investigated mainly for linear problems. This paper is devoted to the study of global convergence of the primal-dual active set method for nonlinear problems with bilateral constraints. Utilizing the close relationship between the primal-dual active set method and semismooth Newton methods, local superlinear convergence of the method is investigated as well.}, number={1}, journal={SIAM JOURNAL ON CONTROL AND OPTIMIZATION}, author={Ito, K and Kunisch, K}, year={2004}, pages={357–376} }
@article{banks_furati_ito_luke_smith_2003, title={Acoustic attenuation employing variable wall admittance}, number={2003}, journal={Directions in mathematical systems theory and optimization (Lecture notes in control and information sciences; 286)}, publisher={New York: Springer}, author={Banks, H. T. and Furati, K. M. and Ito, K. and Luke, N. S. and Smith, C. J.}, editor={A. Rantzer, C. I. ByrnesEditor}, year={2003}, pages={15–26} }
@article{fang_ito_2003, title={Identification of contact regions in semiconductor transistors by level-set methods}, volume={159}, ISSN={["0377-0427"]}, DOI={10.1016/S0377-0427(03)00543-0}, abstractNote={In this paper we present the formulation of level-set methods for the inverse problem of identifying an interface in the coefficient of an elliptic equation from a boundary measurement. This problem arises from the modeling of the identification of contact regions by boundary measurements for semiconductor transistors. We propose the Gauss–Newton direction as the interface velocity, and implement the scheme for a parameterized class of interfaces.}, number={2}, journal={JOURNAL OF COMPUTATIONAL AND APPLIED MATHEMATICS}, author={Fang, WF and Ito, K}, year={2003}, month={Oct}, pages={399–410} }
@article{redfern_fang_ito_musca_dell_faraone_2004, title={Low temperature saturation of p-n junction laser beam induced current signals}, volume={48}, ISSN={["1879-2405"]}, DOI={10.1016/j.sse.2003.09.008}, abstractNote={To date, most studies of the use of laser beam induced current (LBIC) for non-destructive characterisation of photodiodes have been qualitative and/or empirical, due in part to the difficulty of isolating the influence of the large number of material and device parameters on which the LBIC signal is dependent. The development of methodologies whereby these parameters can be determined quantitatively from the LBIC measurements is important for the technique to gain wider acceptance. This work describes, for the first time, the specific experimental conditions under which some of the variable parameters can be eliminated, substantially reducing the complexity of the analysis. In particular, temperature dependence of the peak-to-peak LBIC measurements on p–n junctions is examined for the first time, revealing that a saturation state is reached at low temperatures. When measurements are performed under these saturation conditions, the peak-to-peak LBIC signal becomes independent of doping density and bulk recombination parameters, allowing other parameters including device geometry to be examined with less ambiguity. This concept represents a crucial step towards a quantitative procedure for extraction of p–n junction material and device parameters using LBIC.}, number={3}, journal={SOLID-STATE ELECTRONICS}, author={Redfern, DA and Fang, W and Ito, K and Musca, CA and Dell, JM and Faraone, L}, year={2004}, month={Mar}, pages={409–414} }
@article{borzi_ito_kunisch_2002, title={Optimal control formulation for determining optical flow}, volume={24}, ISSN={["1095-7197"]}, DOI={10.1137/S1064827501386481}, abstractNote={An optimal control formulation for determining optical flow is presented. The new framework differs from preceding approaches in that it does not require differentiation of the data and does combine optical flow with image reconstruction. It can be considered as a control-in-the-coefficients problem with a cost functional of tracking type. A numerical algorithm that solves the optimality system consisting of hyperbolic and elliptic partial differential equations is presented. Numerical experiments demonstrate the effectiveness of the optimal control approach.}, number={3}, journal={SIAM JOURNAL ON SCIENTIFIC COMPUTING}, author={Borzi, A and Ito, K and Kunisch, K}, year={2002}, pages={818–847} }
@article{ito_kunisch_2003, title={Semi-smooth Newton methods for state-constrained optimal control problems}, volume={50}, ISSN={["1872-7956"]}, DOI={10.1016/s0167-6911(03)00156-7}, abstractNote={A regularized optimality system for state-constrained optimal control problems is introduced and semi-smooth Newton methods for its solution are analyzed. Convergence of the regularized problems is proved. Numerical tests confirm the theoretical results and demonstrate the efficiency of the proposed methodology.}, number={3}, journal={SYSTEMS & CONTROL LETTERS}, author={Ito, K and Kunisch, K}, year={2003}, month={Oct}, pages={221–228} }
@article{ito_kunisch_2003, title={Semi-smooth Newton methods for variational inequalities of the first kind}, volume={37}, ISSN={["1290-3841"]}, DOI={10.1051/m2an:2003021}, abstractNote={Semi–smooth Newton methods are analyzed for a class of variational inequalities in infinite dimensions. It is shown that they are equivalent to certain active set strategies. Global and local super-linear convergence are proved. To overcome the phenomenon of finite speed of propagation of discretized problems a penalty version is used as the basis for a continuation procedure to speed up convergence. The choice of the penalty parameter can be made on the basis of an L ∞ estimate for the penalized solutions. Unilateral as well as bilateral problems are considered.}, number={1}, journal={ESAIM-MATHEMATICAL MODELLING AND NUMERICAL ANALYSIS-MODELISATION MATHEMATIQUE ET ANALYSE NUMERIQUE}, author={Ito, K and Kunisch, K}, year={2003}, pages={41–62} }
@article{ito_li_2003, title={Solving a nonlinear problem in magneto-rheological fluids using the immersed interface method}, volume={19}, ISSN={["0885-7474"]}, DOI={10.1023/A:1025356025745}, number={1-3}, journal={JOURNAL OF SCIENTIFIC COMPUTING}, author={Ito, K and Li, ZL}, year={2003}, month={Dec}, pages={253–266} }
@article{deng_ito_li_2003, title={Three-dimensional elliptic solvers for interface problems and applications}, volume={184}, ISSN={["0021-9991"]}, DOI={10.1016/S0021-9991(02)00028-1}, abstractNote={Second-order accurate elliptic solvers using Cartesian grids are presented for three-dimensional interface problems in which the coefficients, the source term, the solution and its normal flux may be discontinuous across an interface. One of our methods is designed for general interface problems with variable but discontinuous coefficient. The scheme preserves the discrete maximum principle using constrained optimization techniques. An algebraic multigrid solver is applied to solve the discrete system. The second method is designed for interface problems with piecewise constant coefficient. The method is based on the fast immersed interface method and a fast 3D Poisson solver. The second method has been modified to solve Helmholtz/Poisson equations on irregular domains. An application of our method to an inverse interface problem of shape identification is also presented. In this application, the level set method is applied to find the unknown surface iteratively.}, number={1}, journal={JOURNAL OF COMPUTATIONAL PHYSICS}, author={Deng, SZ and Ito, K and Li, ZL}, year={2003}, month={Jan}, pages={215–243} }
@article{banks_cole_furati_ito_pinter_2002, title={A computational model for sound field absorption by acoustic arrays}, volume={13}, DOI={10.1106/104538902028631}, number={4}, journal={Journal of Intelligent Material Systems and Structures}, author={Banks, H. T. and Cole, D. G. and Furati, K. M. and Ito, K. and Pinter, G. A.}, year={2002}, pages={231–240} }
@article{borzi_ito_kunisch_2002, title={An optimal control approach to optical flow computation}, volume={40}, ISSN={["0271-2091"]}, DOI={10.1002/fld.273}, abstractNote={AbstractAn optimal control approach for determining optical flow is presented. The new framework differs from preceding approaches in that it does not require differentiation of the data. A numerical algorithm that solves the optimality system consisting of hyperbolic and elliptic partial differential equations is presented. Copyright © 2002 John Wiley & Sons, Ltd.}, number={1-2}, journal={INTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN FLUIDS}, author={Borzi, A and Ito, K and Kunisch, K}, year={2002}, month={Sep}, pages={231–240} }
@article{ito_kunisch_2002, title={Asymptotic properties of receding horizon optimal control problems}, volume={40}, ISSN={["1095-7138"]}, DOI={10.1137/S0363012900369423}, abstractNote={The asymptotic behavior of receding horizon optimal control problems with terminal cost chosen as a control Liapunov function is analyzed for regulator as well as disturbance attenuation problems. Both the continuous as well as the discrete time cases are treated. Further, the approximation of the continuous time optimal control problem by the discrete time receding horizon problems is studied.}, number={5}, journal={SIAM JOURNAL ON CONTROL AND OPTIMIZATION}, author={Ito, K and Kunisch, K}, year={2002}, month={Jan}, pages={1585–1610} }
@book{ito_kappel_2002, title={Evolution equations and approximations}, ISBN={9812380264}, DOI={10.1142/4990}, abstractNote={Dissipative and maximal monotone operators linear semigroups analytic semigroups approximation of C-0 semigroups nonlinear semigroups of contractions locally quasi-dissipative evolution equations the Crandall-Pazy class variational formulations and Gelfand triples applications to concrete systems approximation of solutions for evolution equations semilinear evolution equations. Appendices: some inequalities convergence of Steklov means some technical results needed in Section 9.2.}, publisher={River Edge, NJ: World Scientific}, author={Ito, K. and Kappel, F.}, year={2002} }
@article{fang_ito_2002, title={Nonhomogeneous initial-boundary value problems for nonlinear diffusion-convection equations}, volume={48}, ISSN={["0362-546X"]}, DOI={10.1016/S0362-546X(00)00188-7}, number={2}, journal={NONLINEAR ANALYSIS-THEORY METHODS & APPLICATIONS}, author={Fang, WF and Ito, K}, year={2002}, month={Jan}, pages={303–322} }
@article{ito_kunisch_2002, title={Optimal control of the solid fuel ignition model with H-1-cost}, volume={40}, ISSN={["0363-0129"]}, DOI={10.1137/S0363012900366042}, abstractNote={Optimal control problems for the stationary as well as the time-dependent solid fuel ignition model are investigated. Existence of optimal controls is proved, and optimality systems are derived. The analysis is based on a closedness lemma for the exponential function in L1 and a generalization of Aubin's lemma.}, number={5}, journal={SIAM JOURNAL ON CONTROL AND OPTIMIZATION}, author={Ito, K and Kunisch, K}, year={2002}, month={Jan}, pages={1455–1472} }
@article{fang_ito_redfern_2002, title={Parameter identification for semiconductor diodes by LBIC imaging}, volume={62}, ISSN={["1095-712X"]}, DOI={10.1137/S003613990139249X}, abstractNote={Laser-beam-induced-current (LBIC) imaging is a nondestructive technique used for the characterization of the electrical structure within a semiconductor. In this paper a model is formulated for this technique using the standard drift-diffusion model, and, subsequently, an approximate version and its dual are derived for the study of the inverse problem. The formulation is then applied to a cross-sectional model for n-on-p devices of finite depth to study in detail the relation between the LBIC images and the device parameters. Numerical methods are developed for the simulation of the LBIC image of a diode as well as for the identification of parameters from the LBIC image by least-squares formulation. Numerical examples are presented to illustrate the success of identifying parameters such as junction depth, diffusion length, and equilibrium potential of an abrupt p-n junction diode from its LBIC image. The differentiability of the image with respect to the parameters also is established.}, number={6}, journal={SIAM JOURNAL ON APPLIED MATHEMATICS}, author={Fang, WF and Ito, K and Redfern, DA}, year={2002}, month={Aug}, pages={2149–2174} }
@article{ito_kunisch_2002, title={Receding horizon optimal control for infinite dimensional systems}, volume={8}, ISSN={["1262-3377"]}, DOI={10.1051/cocv:2002032}, abstractNote={The receding horizon control strategy for dynamical systems posed in infinite dimensional spaces is analysed. Its stabilising property is verified provided control Lyapunov functionals are used as terminal penalty functions. For closed loop dissipative systems the terminal penalty can be chosen as quadratic functional. Applications to the Navier–Stokes equations, semilinear wave equations and reaction diffusion systems are given.}, journal={ESAIM-CONTROL OPTIMISATION AND CALCULUS OF VARIATIONS}, author={Ito, K and Kunisch, K}, year={2002}, month={Jun}, pages={741–760} }
@article{hintermuller_ito_kunisch_2003, title={The primal-dual active set strategy as a semismooth Newton method}, volume={13}, ISSN={["1095-7189"]}, DOI={10.1137/S1052623401383558}, abstractNote={This paper addresses complementarity problems motivated by constrained optimal control problems. It is shown that the primal-dual active set strategy, which is known to be extremely efficient for this class of problems, and a specific semismooth Newton method lead to identical algorithms. The notion of slant differentiability is recalled and it is argued that the $\max$-function is slantly differentiable in Lp-spaces when appropriately combined with a two-norm concept. This leads to new local convergence results of the primal-dual active set strategy. Global unconditional convergence results are obtained by means of appropriate merit functions.}, number={3}, journal={SIAM JOURNAL ON OPTIMIZATION}, author={Hintermuller, M and Ito, K and Kunisch, K}, year={2003}, pages={865–888} }
@article{fang_ito_2001, title={An electrochemistry model with nonlinear diffusion: steady-state solutions}, volume={66}, ISSN={["0272-4960"]}, DOI={10.1093/imamat/66.2.195}, abstractNote={We formulate and study the steady-state solutions for an electrochemistry model with nonlinear diffusion. We establish the existence and uniqueness of solutions, prove the global convergence of a successive iteration scheme, and use examples to illustrate the formation of vacuum regions, which is not possible in a linear diffusion model.}, number={2}, journal={IMA JOURNAL OF APPLIED MATHEMATICS}, author={Fang, WF and Ito, K}, year={2001}, month={Apr}, pages={195–213} }
@article{ly_ito_banks_jolly_reitich_2001, title={Dynamic simulation of the temporal response of microstructure formation in magnetorheological fluids}, volume={15}, ISSN={["0217-9792"]}, DOI={10.1142/s0217979201005416}, abstractNote={ Efficient numerical simulations of microstructure development in magnetorheological (MR) fluids are conducted. The simulations, which are based upon a fast multipole algorithm, treat the magnetic inclusions as two-dimensional continuum magnetic entities. The development of microstructure is quantified by computing and recording the time evolution of the effective permeability of the composite fluid. Such a principle has been previously exploited for the experimental measurements of microstructure development [Jolly, Bender and Mathers, ERMR'97, Yonezawa, Japan 1997]. As was observed experimentally, numerical simulations reveal the evolution of microstructure to be multimodal in nature. Unlike the experiments, the numerical simulations afford us the ability to observe the physical mechanisms associated with various modes. }, number={6-7}, journal={INTERNATIONAL JOURNAL OF MODERN PHYSICS B}, author={Ly, HV and Ito, K and Banks, HT and Jolly, MR and Reitich, F}, year={2001}, month={Mar}, pages={894–903} }
@article{ito_2001, title={Existence of solutions to the Hamilton-Jacobi-Bellman equation under quadratic growth conditions}, volume={176}, ISSN={["0022-0396"]}, DOI={10.1006/jdeq.2000.3980}, abstractNote={Abstract In this paper we show the existence of solutions with quadratic growth to Hamilton–Jacobi–Bellman equations. We assume that the Hamiltonian has the quadratic growth both in x and p. We obtain the explicit Lipschitz bound of solutions in the weighted sup-norm. Also, we discuss the vanishing viscosity limit of solutions and show the existence of viscosity solutions to the resulting Hamilton–Jacobi equation.}, number={1}, journal={JOURNAL OF DIFFERENTIAL EQUATIONS}, author={Ito, K}, year={2001}, month={Oct}, pages={1–28} }
@article{fang_ito_2001, title={Existence of stationary solutions to an energy drift-diffusion model for semiconductor devices}, volume={11}, ISSN={["0218-2025"]}, DOI={10.1142/S0218202501001124}, abstractNote={ We analyze a mathematical model for semiconductors derived from the hydrodynamic model under the massless assumption. This model augments the classical drift-diffusion model by including temperature as a dependent variable. We establish the existence of stationary solutions near the equilibrium state. }, number={5}, journal={MATHEMATICAL MODELS & METHODS IN APPLIED SCIENCES}, author={Fang, WF and Ito, K}, year={2001}, month={Jul}, pages={827–840} }
@article{ito_zou_2001, title={Identification of some source densities of the distribution type}, volume={132}, ISSN={["0377-0427"]}, DOI={10.1016/S0377-0427(00)00332-0}, abstractNote={In this paper we investigate the solvability of an ill-posed two-dimensional Fredholm integral equation of the first kind which allows the solutions of distribution type. The problem is first transformed into a well-posed differential–integral equation using output least-squares approach with a regularization of bounded variations. A globally convergent iterative method is proposed and some numerical results are presented. The methodology discussed may be applied for the identification of the boundary shape of the defects of a dielectric material or the interface between different materials.}, number={2}, journal={JOURNAL OF COMPUTATIONAL AND APPLIED MATHEMATICS}, author={Ito, K and Zou, J}, year={2001}, month={Jul}, pages={295–308} }
@article{ito_kunisch_li_2001, title={Level-set function approach to an inverse interface problem}, volume={17}, ISSN={["1361-6420"]}, DOI={10.1088/0266-5611/17/5/301}, abstractNote={A model problem in electrical impedance tomography for the identification of unknown shapes from data in a narrow strip along the boundary of the domain is investigated. The representation of the shape of the boundary and its evolution during an iterative reconstruction process is achieved by the level set method. The shape derivatives of this problem involve the normal derivative of the potential along the unknown boundary. Hence an accurate resolution of its derivatives along the unknown interface is essential. It is obtained by the immersed interface method.}, number={5}, journal={INVERSE PROBLEMS}, author={Ito, K and Kunisch, K and Li, ZL}, year={2001}, month={Oct}, pages={1225–1242} }
@article{li_ito_2001, title={Maximum principle preserving schemes for interface problems with discontinuous coefficients}, volume={23}, ISSN={["1064-8275"]}, DOI={10.1137/S1064827500370160}, abstractNote={New finite difference methods using Cartesian grids are developed for elliptic interface problems with variable discontinuous coefficients, singular sources, and nonsmooth or even discontinuous solutions. The new finite difference schemes are constructed to satisfy the sign property of the discrete maximum principle using quadratic optimization techniques. The methods are shown to converge under certain conditions using comparison functions. The coefficient matrix of the resulting linear system of equations is an M-matrix and is coupled with a multigrid solver. Numerical examples are also provided to show the efficiency of the proposed methods.}, number={1}, journal={SIAM JOURNAL ON SCIENTIFIC COMPUTING}, author={Li, ZL and Ito, K}, year={2001}, month={Jun}, pages={339–361} }
@article{banks_choi_durso_ito_2001, title={Nonlinear exothermic contributions to radio-frequency bonding of adhesives}, volume={2}, ISSN={["1468-1218"]}, DOI={10.1016/S0362-546X(00)00110-3}, abstractNote={This work describes an e ort to model the radio-frequency curing of epoxy adhesives in bonding of composites.We present a model based on the three-dimensional heat equation which includes nonlinear heat generating terms.A constructive proof of existence and uniqueness of solutions to our governing equations is given, providing a framework for the development of a computational method.Furthermore, using experimental data, we apply the numerical method to study the importance of the nonlinear contributions of an internal exothermic reaction which takes place as the adhesive cures.}, number={3}, journal={NONLINEAR ANALYSIS-REAL WORLD APPLICATIONS}, author={Banks, HT and Choi, MG and Durso, SR and Ito, K}, year={2001}, month={Sep}, pages={357–386} }
@article{ito_ravindran_2001, title={Reduced basis method for optimal control of unsteady viscous flows}, volume={15}, ISSN={["1061-8562"]}, DOI={10.1080/10618560108970021}, abstractNote={Abstract In this article we discuss the reduced basis method (RBM) for optimal control of unsteady viscous flows. RBM is a reduction method in which one can achieve the versatility of the finite element method or another for that matter and gain significant reduction in the number of degrees of freedom. The essential idea in this method is to define a reduced order subspace spanned by few basis elements and then obtain the solution via a Galerkin projection. We present several ways to define this subspace. Feasibility of the approach is demonstrated on two boundary control problems in cavity and wall bounded channel flows. Control action is effected through boundary surface movement on part of the solid wall. Application of RBM to the control problems leads to finite dimensional optimal control problems which are solved using Newton's method. Through computational experiments we demonstrate the feasibility and applicability of the reduced basis method for control of unsteady viscous flows.}, number={2}, journal={INTERNATIONAL JOURNAL OF COMPUTATIONAL FLUID DYNAMICS}, author={Ito, K and Ravindran, SS}, year={2001}, pages={97–113} }
@article{ito_schroeter_2001, title={Reduced order feedback synthesis for viscous incompressible flows}, volume={33}, ISSN={["0895-7177"]}, DOI={10.1016/S0895-7177(00)00237-5}, abstractNote={We discuss the application of the reduced basis method for the simulation and control of unsteady viscous flows governed by the incompressible Navier-Stokes equations. We describe how to use this method in terms of the construction of a lower-order compensator design. Our approach includes a construction method of the optimal state feedback law for finite-dimensional nonlinear regulator problems. The method is applied to construct a feedback law for the reduced order control model of the Navier-Stokes equations, and then we apply our feedback law to the original control system. Our method is demonstrated on a control problem formulated in a channel flow using a boundary velocity control. We also show how these ideas can be extended to control problems governed by partial differential equations. Numerical results are reported for the open and closed loop controls, and a compensator design is proposed to complete the closed loop dynamics.}, number={1-3}, journal={MATHEMATICAL AND COMPUTER MODELLING}, author={Ito, K and Schroeter, JD}, year={2001}, pages={173–192} }
@article{simon_reitich_jolly_ito_banks_2001, title={The effective magnetic properties of magnetorheological fluids}, volume={33}, ISSN={["0895-7177"]}, DOI={10.1016/S0895-7177(00)00244-2}, abstractNote={Magnetorheological (MR) fluids represent a class of smart materials whose rheological properties change in response to the application of a magnetic field. These fluids typically consist of small (μm) magnetizable particles dispersed in a nonmagnetic carrier fluid that generally contains additives such as surfactants and antiwear agents [1]. Due to such additives, there is an outer nonmagnetic layer on the particles that keeps them from touching. The goal of this paper is to study the effective magnetic behavior of an MR composite as a function of the interparticle distance. To this end, we present and employ a model for the effective magnetic properties of MR fluids with periodic microstructure that is based on the theory of homogenization. Finally, we discuss an interpolating formula for the effective permeability of MR fluids as an extension of the work of Keller [2] and Doyle [3].}, number={1-3}, journal={MATHEMATICAL AND COMPUTER MODELLING}, author={Simon, TM and Reitich, F and Jolly, MR and Ito, K and Banks, HT}, year={2001}, pages={273–284} }
@article{oostveen_curtain_ito_2000, title={An approximation theory or strongly stabilizing solutions to the operator LQ Riccati equation}, volume={38}, ISSN={["0363-0129"]}, DOI={10.1137/S0363012998339691}, abstractNote={The linear-quadratic (LQ) control problem is considered for a class of infinite-dimensional systems with bounded input and output operators, that are not exponentially stabilizable, but only strongly stabilizable. A sufficient condition for the existence of a minimizing control and of a stabilizing solution to the associated LQ Riccati equation is given. The main contribution of this paper is the convergence of the stabilizing solutions of a sequence of finite-dimensional Riccati equations to the strongly stabilizing solution of the infinite-dimensional Riccati equation. The result is applied to a model of propagation of sound waves in a one-dimensional wave-guide.}, number={6}, journal={SIAM JOURNAL ON CONTROL AND OPTIMIZATION}, author={Oostveen, JC and Curtain, RF and Ito, K}, year={2000}, month={Aug}, pages={1909–1937} }
@article{ito_rozovskii_2000, title={Approximation of the Kushner equation for nonlinear filtering}, volume={38}, ISSN={["0363-0129"]}, DOI={10.1137/S0363012998344270}, abstractNote={In this paper we discuss the well-posedness and approximation of solutions to the Kushner equation in nonlinear filtering problems. We develop and analyze a time integration method based on the operator splitting. Also, we discuss its relation to the operator-splitting method for the Zakai equation.}, number={3}, journal={SIAM JOURNAL ON CONTROL AND OPTIMIZATION}, author={Ito, K and Rozovskii, B}, year={2000}, month={Mar}, pages={893–915} }
@article{ito_kunisch_2000, title={Augmented Lagrangian methods for nonsmooth, convex optimization in Hilbert spaces}, volume={41}, ISSN={["0362-546X"]}, DOI={10.1016/S0362-546X(98)00299-5}, number={5-6}, journal={NONLINEAR ANALYSIS-THEORY METHODS & APPLICATIONS}, author={Ito, K and Kunisch, K}, year={2000}, month={Aug}, pages={591–616} }
@article{ito_kunisch_2000, title={BV-type regularization methods for convoluted objects with edge, flat and grey scales}, volume={16}, ISSN={["0266-5611"]}, DOI={10.1088/0266-5611/16/4/303}, abstractNote={A variational approach for the robust inversion of linear smoothing operators is discussed. We employ and generalize the enhancement techniques based on BV- and Perona-Malik-type regularization methods. The problem is cast as the minimization of a cost functional consisting of a data fitting and a restoration energy criterion for multiscale objects consisting of edge, flat and grey regions. An iterative algorithm for finding the restored object that minimizes the cost functional is developed and analysed. It is based upon a fixed-point iteration combining a time-marching and successive substitution method for finding a solution to a quasi-elliptic partial differential equation. Global convergence is proved. Numerical examples illustrate the proposed approach.}, number={4}, journal={INVERSE PROBLEMS}, author={Ito, K and Kunisch, K}, year={2000}, month={Aug}, pages={909–928} }
@article{fang_ito_2001, title={Existence and uniqueness of steady-state solutions for an electrochemistry model}, volume={129}, ISSN={["0002-9939"]}, DOI={10.1090/S0002-9939-00-05769-5}, abstractNote={We present a simple proof for the existence and uniqueness of steady-state solutions to an electrochemistry model with multiple species.}, number={4}, journal={PROCEEDINGS OF THE AMERICAN MATHEMATICAL SOCIETY}, author={Fang, WF and Ito, K}, year={2001}, pages={1037–1040} }
@article{ito_xiong_2000, title={Gaussian filters for nonlinear filtering problems}, volume={45}, ISSN={["0018-9286"]}, DOI={10.1109/9.855552}, abstractNote={We develop and analyze real-time and accurate filters for nonlinear filtering problems based on the Gaussian distributions. We present the systematic formulation of Gaussian filters and develop efficient and accurate numerical integration of the optimal filter. We also discuss the mixed Gaussian filters in which the conditional probability density is approximated by the sum of Gaussian distributions. A new update rule of weights for Gaussian sum filters is proposed. Our numerical tests demonstrate that new filters significantly improve the extended Kalman filter with no additional cost, and the new Gaussian sum filter has a nearly optimal performance.}, number={5}, journal={IEEE TRANSACTIONS ON AUTOMATIC CONTROL}, author={Ito, K and Xiong, KQ}, year={2000}, month={May}, pages={910–927} }
@article{ito_kunisch_2000, title={Newton's method for class of weakly singular optimal control problems}, volume={10}, ISSN={["1052-6234"]}, DOI={10.1137/S1052623497320840}, abstractNote={Newton's method for optimal control of highly nonlinear partial differential equations is analyzed using a 2-norm technique. We consider the case where neither the linearization of the equality constraint e characterizing the differential equation is surjective nor a second order sufficient optimality condition holds for the topology on which e is well defined. Such problems occur, for instance, in optimal control of semilinear elliptic equations or for parameter estimation problems. Despite the above mentioned difficulties, sufficient conditions for second order convergence are obtained.}, number={3}, journal={SIAM JOURNAL ON OPTIMIZATION}, author={Ito, K and Kunisch, K}, year={2000}, month={Jun}, pages={896–916} }
@article{ito_kunisch_2000, title={Optimal control of elliptic variational inequalities}, volume={41}, ISSN={["0095-4616"]}, DOI={10.1007/s002459911017}, number={3}, journal={APPLIED MATHEMATICS AND OPTIMIZATION}, author={Ito, K and Kunisch, K}, year={2000}, pages={343–364} }
@article{woods_dietz_ito_lauko_2000, title={Real-time thickness and compositional control of Ga1-xInxP growth using p-polarized reflectance}, volume={18}, ISSN={["0734-2101"]}, DOI={10.1116/1.582469}, abstractNote={Advances in the engineering and design of advanced electro-optical materials require sensors and control strategies that allow tight control over thickness and composition of multilayered structures. In response to this demand, we developed and applied p-polarized reflectance (PR) for real-time optical characterization and control of heteroepitaxial GaP/GaInP growth under pulsed chemical beam epitaxy conditions. For closed-loop control, we applied nonlinear control algorithms (based on nonlinear Kalman filtering) that utilizes the PR signals to adjust the source flows involved in the heteroepitaxial growth of Ga1−xInxP on Si(001). A reduced order surface kinetics model has been formulated to establish the linkage between the surface reaction kinetic and its optical response. These data are linked to compute the compositional and thickness change per time unit, utilizing the monitored PR signals for validation. This allows the establishment of feedback control algorithms, able to control both the growth rate and composition of Ga1−xInxP heterostructures.}, number={4}, journal={JOURNAL OF VACUUM SCIENCE & TECHNOLOGY A-VACUUM SURFACES AND FILMS}, author={Woods, V and Dietz, N and Ito, K and Lauko, I}, year={2000}, pages={1190–1195} }
@article{fang_ito_2000, title={Weak solutions for diffusion-convection equations}, volume={13}, ISSN={["0893-9659"]}, DOI={10.1016/S0893-9659(99)00188-3}, abstractNote={Weak solutions to diffusion-convection equations with less regular convective field and boundary data are shown to exist as limits of solutions to problems with mixed boundary conditions.}, number={3}, journal={APPLIED MATHEMATICS LETTERS}, author={Fang, W and Ito, K}, year={2000}, month={Apr}, pages={69–75} }
@article{ito_reitich_1999, title={A high-order perturbation approach to profile reconstruction: I. Perfectly conducting gratings}, volume={15}, ISSN={["0266-5611"]}, DOI={10.1088/0266-5611/15/4/315}, abstractNote={A new method for the reconstruction of two-dimensional periodic structures from scattered far-field data is presented. The approach is based on the recently developed `methods of variation of boundaries' (MVB) for the solution of forward-scattering problems. Here, the inverse problem is formulated as that of minimization of an appropriate nonlinear least-squares cost functional J. The analytic continuation ideas inherent to MVB are then advanced to enable a global line search at each step of a proposed conjugate gradients algorithm. Through a number of numerical examples it is demonstrated that such globalization may be necessary to overcome the non-convexity of J which, in turn, is shown to persist even when the global minimizer is known to be unique.}, number={4}, journal={INVERSE PROBLEMS}, author={Ito, K and Reitich, F}, year={1999}, month={Aug}, pages={1067–1085} }
@article{ito_kunisch_1999, title={An active set strategy based on the augmented Lagrangian formulation for image restoration}, volume={33}, DOI={10.1051/m2an:1999102}, abstractNote={Lagrangian and augmented Lagrangian methods for nondifferentiable
optimization problems that arise from the total bounded variation formulation of image restoration problems are analyzed. Conditional convergence of the
Uzawa algorithm and unconditional convergence of the first order augmented
Lagrangian schemes are discussed. A Newton type method based on an active
set strategy defined by means of the dual variables is developed and
analyzed. Numerical examples for blocky signals and images perturbed
by very high noise are included.}, number={1}, journal={RAIRO. Mathematical Modelling and Numerical Analysis}, author={Ito, K. and Kunisch, K.}, year={1999}, pages={1–21} }
@article{simon_ito_banks_reitich_jolly_1999, title={Estimation of the effective permeability in magnetorheological fluids}, volume={10}, ISSN={["1045-389X"]}, DOI={10.1106/6KW6-7V12-NRQ3-BW6V}, abstractNote={ Magnetorheological (MR) fluids constitute examples of controllable ("smart") fluids, whose Theological properties vary in response to an applied magnetic field. These fluids typically consist of micron-sized, magnetizable particles dispersed in a nonpermeable carrier fluid. The essential characteristic of MR fluids is that they may be continuously and reversibly varied from a state of free flowing liquids in the absence of an applied magnetic field to that of stiff semi-solids in a moderate field. Understanding the magnetic properties of MR fluids is crucial to the design of MR fluid-based devices and it also provides valuable insight into the character of the microstructure responsible for their field-dependent rheology. Prediction of the overall magnetic properties of MR composites is a challenging task, however, due to the highly nonlinear and strongly spatially variable nature of the magnetization of the constituents. In this paper we propose a model for this behavior that is based on the mathematical theory of homogenization. We derive effective equations that govern the magnetic response of (periodically arranged) particle-chains through magnetic saturation. Comparisons of numerical results for these equations with experimental data show good agreement which suggests that our approach could be useful in the design of improved MR fluids. }, number={11}, journal={JOURNAL OF INTELLIGENT MATERIAL SYSTEMS AND STRUCTURES}, author={Simon, TM and Ito, K and Banks, HT and Reitich, F and Jolly, MR}, year={1999}, month={Nov}, pages={872–879} }
@article{bergounioux_ito_kunisch_1999, title={Primal-dual strategy for constrained optimal control problems}, volume={37}, ISSN={["0363-0129"]}, DOI={10.1137/S0363012997328609}, abstractNote={An algorithm for efficient solution of control constrained optimal control problems is proposed and analyzed. It is based on an active set strategy involving primal as well as dual variables. For discretized problems sufficient conditions for convergence in finitely many iterations are given. Numerical examples are given and the role of the strict complementarity condition is discussed.}, number={4}, journal={SIAM JOURNAL ON CONTROL AND OPTIMIZATION}, author={Bergounioux, M and Ito, K and Kunisch, K}, year={1999}, month={May}, pages={1176–1194} }
@article{dietz_woods_ito_lauko_1999, title={Real-time optical control of Ga1-xInxP film growth by p-polarized reflectance}, volume={17}, ISSN={["1520-8559"]}, DOI={10.1116/1.581811}, abstractNote={The engineering of advanced optoelectronic integrated circuits implies the stringent control of thickness and composition. These demands led to the development of surface-sensitive real-time optical sensors that are able to move the control point close to the point where the growth occurs, which in a chemical beam epitaxy process is the surface reaction layer, built up of physisorbed and chemisorbed precursor fragments between the ambient and film interface. In this context, we explored the application of p-polarized reflectance spectroscopy (PRS) for real-time monitoring and control of pulsed chemical beam epitaxy during low-temperature growth of epitaxial Ga1−xInxP heterostructures on Si(001) substrates. A reduced order surface kinetics model has been developed to describe the decomposition and growth kinetics of the involved organometallic precursors and their incorporation in the film deposition. We demonstrate the linkage of the PRS response towards the surface reaction chemistry, composition, film growth rate, and film properties. Mathematical control algorithms are applied that link the PR signals to the growth process control parameters to control the composition and growth rate of epitaxial Ga1−xInxP heterostructures.}, number={4}, journal={JOURNAL OF VACUUM SCIENCE & TECHNOLOGY A}, author={Dietz, N and Woods, V and Ito, K and Lauko, I}, year={1999}, pages={1300–1306} }
@article{ly_reitich_jolly_banks_ito_1999, title={Simulations of particle dynamics in magnetorheological fluids}, volume={155}, ISSN={["1090-2716"]}, DOI={10.1006/jcph.1999.6335}, abstractNote={We present particle dynamics simulations for the response of magnetorheological (MR) fluids upon application of a magnetic field. The particles motion is considered to be governed by magnetic, hydrodynamic, and repulsive interactions. Fluid-particle interactions are accounted for via Stokes' drag while inter-particle repulsions are modeled through approximate hard-sphere rejections. In accordance with their greater significance, on the other hand (linear) magnetic interactions are fully simulated. The time evolution is considered to be magnetically quasi-static and magnetostatic forces are derived from the solution of (steady) Maxwell's equations, recomputed at each instant in time. For this we use a potential theoretic formulation where the boundary integral equations are solved with a fast multipole approach. We show that the resulting numerical codes can be effectively used to study a number of experimental observables such as effective magnetic permeabilities and response time-scales which are of crucial importance in the design of MR fluids.}, number={1}, journal={JOURNAL OF COMPUTATIONAL PHYSICS}, author={Ly, HV and Reitich, E and Jolly, MR and Banks, HT and Ito, K}, year={1999}, month={Oct}, pages={160–177} }
@article{ito_ravindran_1998, title={A reduced-order method for simulation and control of fluid flows}, volume={143}, ISSN={["1090-2716"]}, DOI={10.1006/jcph.1998.5943}, abstractNote={This article presents a reduced-order modeling approach for simulation and control of viscous incompressible flows. The reduced-order models suitable for control and which capture the essential physics are developed using the reduced-basis method. The so-called Lagrange approach is used to define reduced bases and the basis functions in this approach are obtained from the numerical solutions. The feasibility of this method for flow control is demonstrated on boundary control problems in closed cavity and in wall-bounded channel flows. Control action is effected through boundary surface movement on a part of the solid wall. Our formulation of the reduced-order method applied to flow control problems leads to a constrained minimization problem and is solved by applying Newton-like methods to the necessary conditions of optimality. Through our computational experiments we demonstrate the feasibility and applicability of the reduced-order method for simulation and control of fluid flows.}, number={2}, journal={JOURNAL OF COMPUTATIONAL PHYSICS}, author={Ito, K and Ravindran, SS}, year={1998}, month={Jul}, pages={403–425} }
@article{ito_morris_1998, title={An approximation theory of solutions to operator Riccati equations for H(infinity) control}, volume={36}, ISSN={["0363-0129"]}, DOI={10.1137/S0363012994274422}, abstractNote={As in the finite-dimensional case, the appropriate state feedback for the infinite-dimensional $H^\infty$ disturbance-attenuation problem may be calculated by solving a Riccati equation. This operator Riccati equation can rarely be solved exactly. We approximate the original infinite-dimensional system by a sequence of finite-dimensional systems and consider the corresponding finite-dimensional disturbance-attenuation problems. We make the same assumptions required in approximations for the classical linear quadratic regulator problem and show that the sequence of solutions to the corresponding finite-dimensional Riccati equations converge strongly to the solution to the infinite-dimensional Riccati equation. Furthermore, the corresponding finite-dimensional feedback operators yield performance arbitrarily close to that obtained with the infinite-dimensional solution.}, number={1}, journal={SIAM JOURNAL ON CONTROL AND OPTIMIZATION}, author={Ito, K and Morris, KA}, year={1998}, month={Jan}, pages={82–99} }
@article{ito_ravindran_1998, title={Optimal control of thermally convected fluid flows}, volume={19}, ISSN={["1064-8275"]}, DOI={10.1137/S1064827596299731}, abstractNote={We examine the optimal control of stationary thermally convected fluid flows from the theoretical and numerical point of view. We use thermal convection as control mechanism; that is, control is effected through the temperature on part of the boundary. Control problems are formulated as constrained minimization problems. Existence of optimal control is given and a first-order necessary condition of optimality from which optimal solutions can be obtained is established. We develop numerical methods to solve the necessary condition of optimality and present computational results for control of cavity- and channel-type flows showing the feasibility of the proposed approach.}, number={6}, journal={SIAM JOURNAL ON SCIENTIFIC COMPUTING}, author={Ito, K and Ravindran, SS}, year={1998}, month={Nov}, pages={1847–1869} }
@article{bachmann_sukidi_hopfner_harris_dietz_tran_beeler_ito_banks_1998, title={Real-time monitoring of steady-state pulsed chemical beam epitaxy by p-polarized reflectance}, volume={183}, ISSN={["0022-0248"]}, DOI={10.1016/s0022-0248(97)00410-7}, abstractNote={The structure in the p-polarized reflectance (PR) intensity Rp4(t) - observed under conditions of pulsed chemical beam epitaxy (PCBE) - is modeled on the basis of the four-layer stack: ambient/surface reaction layer (SRL)/epilayer/substrate. Linearization of the PR intensity with regard to the phase factor associated with the SRL results in a good approximation that can be expressed as Rp4 = Rp3 + ΔRp.Rp3 is the reflectivity of the three-layer stack ambient-epilayer-substrate. ΔRp describes the properties of the SRL. An explicit relation is derived between ΔRp(t) and the time-dependent surface concentrations ch(t) (h = 1, 2, …, N) of the constituents of the SRL, which holds for conditions of submonolayer coverage of the surface by source vapor molecules. Under conditions of low temperature PCBE at high flux, the SRL is expected to exhibit nonideal behavior, mandating replacement of the surface concentrations by activities. Also, in this case, the thickness of the SRL must be represented in terms of partial molar volumina Vh. Since the relation between ΔRp(t) and the activities of reactants, intermediates and products of the chemical reactions driving heteroepitaxial growth is non-linear, the extraction of kinetic parameters from the measured time dependence of the PR signal generally requires numerical modeling.}, number={3}, journal={JOURNAL OF CRYSTAL GROWTH}, author={Bachmann, KJ and Sukidi, N and Hopfner, C and Harris, C and Dietz, N and Tran, HT and Beeler, S and Ito, K and Banks, HT}, year={1998}, month={Jan}, pages={323–337} }
@article{dietz_ito_1998, title={Real-time optical characterization of GaP heterostructures by p-polarized reflectance}, volume={313}, ISSN={["0040-6090"]}, DOI={10.1016/S0040-6090(97)00896-1}, abstractNote={The stringent tolerances in the engineering of advanced optoelectronic integrated circuits with respect to control thickness and composition of ultra-thin layers require the development of monitoring and control techniques that follow the deposition process with sub-monolayer resolution. These demands led to the development of surface-sensitive real-time optical sensors that are able to move the control point close to the point where the growth occurs, which in a chemical beam epitaxy process is the surface reaction layer, built up of physisorbed and chemisorbed precursor fragments between the ambient and film interface. In this contribution, we explore the application of p-polarized reflectance spectroscopy (PRS) in the context of real-time monitoring and control of pulsed chemical beam epitaxy (PCBE) during low temperature growth of epitaxial GaP heterostructures on Si(001) substrates by PCBE. The effect of periodic alterations in composition and thickness of a surface reaction layer (SRL) is monitored by PRS as a periodic modulated reflectance amplitude, denoted as fine structure. Using a `reduced order kinetic model' we demonstrate the linkage of the PRS response towards surface reaction chemistry, film growth rate, and film properties. Mathematical control algorithms are introduced that link the PR signals to the growth process control parameters.}, journal={THIN SOLID FILMS}, author={Dietz, N and Ito, K}, year={1998}, month={Feb}, pages={614–619} }
@article{ito_kappel_1998, title={The Trotter-Kato theorem and approximation of PDEs}, volume={67}, ISSN={["0025-5718"]}, DOI={10.1090/S0025-5718-98-00915-6}, abstractNote={We present formulations of the Trotter-Kato theorem for approximation of linear C
0
{}_0
-semigroups which provide very useful framework when convergence of numerical approximations to solutions of PDEs are studied. Applicability of our results is demonstrated using a first order hyperbolic equation, a wave equation and Stokes’ equation as illustrative examples.}, number={221}, journal={MATHEMATICS OF COMPUTATION}, author={Ito, K and Kappel, F}, year={1998}, month={Jan}, pages={21–44} }
@article{ito_yan_1998, title={Viscous scalar conservation law with nonlinear flux feedback and global attractors}, volume={227}, ISSN={["0022-247X"]}, DOI={10.1006/jmaa.1998.6016}, abstractNote={Abstract In this paper we study the forced viscous scalar conservation law on (0, 1) with the nonlinear flux feedback at the boundary. Global existence and uniqueness are established for L ∞ bounded initial conditions and forcing functions. Under an appropriate growth condition on the flux function and nonlinear dissipation at the boundary, we show the existence of an absorbing set that absorbs the whole space L ∞ (0, 1), and the existence of a compact global attractor in the L ∞ topology.}, number={1}, journal={JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS}, author={Ito, K and Yan, Y}, year={1998}, month={Nov}, pages={271–299} }
@article{ito_kunisch_1997, title={Estimation of the convection coefficient in elliptic equations}, volume={13}, ISSN={["0266-5611"]}, DOI={10.1088/0266-5611/13/4/007}, abstractNote={The parameter estimation problem for the convection coefficient in elliptic equations is considered in the class of -vector fields. The optimality system is characterized and the convergence of the gradient method is proved. To apply the SQP-method to the singular optimality system, a modification involving a feasibility step in the primal and dual variables is introduced. The resulting algorithm has a second-order convergence rate. Numerical experiments are included.}, number={4}, journal={INVERSE PROBLEMS}, author={Ito, K and Kunisch, K}, year={1997}, month={Aug}, pages={995–1013} }
@article{bachmann_hopfner_sukidi_miller_harris_aspnes_dietz_tran_beeler_ito_et al._1997, title={Molecular layer epitaxy by real-time optical process monitoring}, volume={112}, DOI={10.1016/S0169-4332(96)00975-0}, abstractNote={In this paper we consider modern methods of optical process monitoring and control in the context of atomic layer epitaxy. One specific method, p-polarized reflectance spectroscopy (PRS), is chosen to assess details of layer-by-layer growth. We show that PRS monitoring under conditions of steady-state growth by pulsed chemical beam epitaxy (PCBE) can achieve the deposition of molecular layers of GaP on silicon (100) deposited with a precision of 5%, which can be improved by reducing the growth rate and increasing the period of time averaging of the reflectance data. Since in the nucleation period prior to formation of a contiguous heteroepitaxial film inhomogeneous surface chemistry and roughening complicates the modeling of the overgrowth process, advances in both experimental methods and theory are required for extending the control to non-steady-state growth conditions. Results of simultaneous single-wavelength PR monitoring and laser light scattering measurements in conjunction with atomic force microscopy studies of short period heteroepitaxial overgrowth processes are presented. The extension of PRS to the monitoring of organometallic chemical vapor deposition at higher pressures is also discussed.}, number={1997 Mar.}, journal={Applied Surface Science}, author={Bachmann, K. J. and Hopfner, C. and Sukidi, N. and Miller, A. E. and Harris, C. J. and Aspnes, D. E. and Dietz, N. A. and Tran, Hien and Beeler, S. C. and Ito, K. and et al.}, year={1997}, pages={38–47} }
@article{fang_ito_1997, title={On the inhomogeneous system of isentropic gas dynamics by the viscosity method}, volume={127}, ISSN={["0308-2105"]}, DOI={10.1017/s0308210500023647}, abstractNote={The existence of global weak solutions is shown for the equations of isentropic gas dynamics with inhomogeneous terms by the viscosity method. A generalised version of the method of invariant regions is developed to obtain the uniform L∞ bounds of the viscosity solutions, and the method of compensated compactness is applied to show the existence of weak solutions as limits of the viscosity solutions. The lower positive bound for the density function is also obtained. As an example, a hydrodynamic model for semiconductors is analysed}, journal={PROCEEDINGS OF THE ROYAL SOCIETY OF EDINBURGH SECTION A-MATHEMATICS}, author={Fang, WF and Ito, K}, year={1997}, pages={261–280} }
@article{fang_ito_1997, title={Steady-state solutions of a one-dimensional hydrodynamic model for semiconductors}, volume={133}, ISSN={["0022-0396"]}, DOI={10.1006/jdeq.1996.3203}, abstractNote={Abstract Steady-state BV solutions to a one-dimensional hydrodynamic model for semiconductors are shown to exist as limits of viscous solutions as the viscosity vanishes.}, number={2}, journal={JOURNAL OF DIFFERENTIAL EQUATIONS}, author={Fang, WF and Ito, K}, year={1997}, month={Jan}, pages={224–244} }
@article{fang_ito_1997, title={Weak solutions to a one-dimensional hydrodynamic model of two carrier types for semiconductors}, volume={28}, ISSN={["0362-546X"]}, DOI={10.1016/0362-546X(95)00189-3}, number={5}, journal={NONLINEAR ANALYSIS-THEORY METHODS & APPLICATIONS}, author={Fang, WF and Ito, K}, year={1997}, month={Mar}, pages={947–963} }