@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 element discretization scheme is applied to the equation system leading to fourth-order phase accuracy and thereby reducing the pollution error considerably. The resulting linear system is solved with the GMRES method using a multiplicative nonoverlapping domain decomposition preconditioner with layers defining the subdomains. This right preconditioner is constructed by embedding each layer into a rectangular domain and by employing a fast direct solver. Due to the construction of the preconditioner the iterations can be reduced to a subspace corresponding to the interfaces between the layers. Numerical experiments with several test cases demonstrate the effectiveness and scalability of the proposed method and ability to solve large-scale problems with up to billions of unknowns.}, number={5}, journal={SIAM JOURNAL ON SCIENTIFIC COMPUTING}, author={Heikkola, Erkki and Ito, Kazufumi and Toivanen, Jari}, year={2019}, pages={C505–C521} }
@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{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} }
@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{neri_toivanen_makinen_2007, title={An adaptive evolutionary algorithm with intelligent mutation local searchers for designing multidrug therapies for HIV}, volume={27}, ISSN={["1573-7497"]}, DOI={10.1007/s10489-007-0069-8}, number={3}, journal={APPLIED INTELLIGENCE}, author={Neri, Ferrante and Toivanen, Jari and Makinen, Raino A. E.}, year={2007}, month={Dec}, pages={219–235} }
@article{lehtovaara_toivanen_eloranta_2007, title={Solution of time-independent Schrodinger equation by the imaginary time propagation method}, volume={221}, ISSN={["1090-2716"]}, DOI={10.1016/j.jcp.2006.06.006}, abstractNote={Numerical solution of eigenvalues and eigenvectors of large matrices originating from discretization of linear and non-linear Schrödinger equations using the imaginary time propagation (ITP) method is described. Convergence properties and accuracy of 2nd and 4th order operator-splitting methods for the ITP method are studied using numerical examples. The natural convergence of the method is further accelerated with a new dynamic time step adjustment method. The results show that the ITP method has better scaling with respect to matrix size as compared to the implicitly restarted Lanczos method. An efficient parallel implementation of the ITP method for shared memory computers is also demonstrated.}, number={1}, journal={JOURNAL OF COMPUTATIONAL PHYSICS}, author={Lehtovaara, L. and Toivanen, J. and Eloranta, J.}, year={2007}, month={Jan}, pages={148–157} }
@article{banks_kwon_toivanen_tran_2006, title={A state-dependent Riccati equation-based estimator approach for HIV feedback control}, volume={27}, ISSN={["1099-1514"]}, DOI={10.1002/oca.773}, abstractNote={We consider optimal dynamic multidrug therapies for human immunodeficiency virus (HIV) type 1 infection. In this context, we describe an optimal tracking problem attempting to drive the states of the system to a stationary state in which the viral load is low and the immune response is strong. We consider optimal feedback control with full-state as well as with partial-state measurements. In the case of partial-state measurement, a state estimator is constructed based on viral load and T-cell count measurements. We demonstrate by numerical simulations that by anticipation of and response to the disease progression, the dynamic multidrug strategy reduces the viral load, increases the CD4+ T-cell count and improves the immune response. Copyright © 2006 John Wiley & Sons, Ltd.}, number={2}, journal={OPTIMAL CONTROL APPLICATIONS & METHODS}, author={Banks, HT and Kwon, HD and Toivanen, JA and Tran, HT}, year={2006}, pages={93–121} }
@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 airfoil) in which we report our findings in the form of reduced radar cross sections (RCS)\@.}, 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{glowinski_toivanen_2005, title={A multigrid preconditioner and automatic differentiation for non-equilibrium radiation diffusion problems}, volume={207}, ISSN={["1090-2716"]}, DOI={10.1016/j.jcp.2005.01.032}, abstractNote={We study the efficient solution of non-equilibrium radiation diffusion problems. An implicit time discretization leads to the solution of systems of non-linear equations which couple radiation energy and material temperature. We consider the implicit Euler method, the mid-point scheme, the two-step backward differentiation formula, and a two-stage implicit Runge-Kutta method for time discretization. We employ a Newton-Krylov method in the solution of arising non-linear problems. We describe the computation of the Jacobian matrix for Newton's method using automatic differentiation based on the operator overloading in Fortran 90. For GMRES iterations, we propose a simple multigrid preconditioner applied directly to the coupled linearized problems. We demonstrate the efficiency and scalability of the proposed solution procedure by solving one-dimensional and two-dimensional model problems.}, number={1}, journal={JOURNAL OF COMPUTATIONAL PHYSICS}, author={Glowinski, R and Toivanen, J}, year={2005}, month={Jul}, pages={354–374} }