TY - RPRT TI - Industrial Mathematics Modeling Workshop for Graduate Students Series DA - 2000/// PY - 2000/// M3 - CRSC Technical Reports ER - TY - BOOK TI - Industrial Mathematics A3 - Gremaud, P. A3 - Li, Zhilin A3 - Smith, R A3 - Tran, H. DA - 2000/// PY - 2000/// PB - SIAM SN - O-89871-467-2 ER - TY - BOOK TI - Industrial Mathematics: The 1998 CRSC Workshop A3 - Gremaud, P.A. A3 - Li, Z. A3 - Smith, R.C. A3 - Tran, H.T. DA - 2000/10// PY - 2000/10// SP - 70 PB - SIAM Publications ER - TY - BOOK TI - Industrial Mathematics: The 1998 CRSC Workshop DA - 2000/// PY - 2000/// PB - SIAM ER - TY - JOUR TI - Nonreflecting artificial boundary conditions for the replacement of rejected equations with gaps T2 - Mat. Model. DA - 2000/// PY - 2000/// VL - 12 IS - 12 SP - 108-127 UR - https://mathscinet.ams.org/mathscinet-getitem?mr=1833776 N1 - [in Russian] RN - [in Russian] ER - TY - JOUR TI - Global Artificial Boundary Conditions for Computation of External Flows with Jets AU - Tsynkov, Semyon AU - Abarbanel, Saul AU - Nordström, Jan AU - Ryaben'kii, Victor AU - Vatsa, Veer T2 - AIAA Journal AB - We propose new global artificial boundary conditions (ABCs) for computation of flows with propulsive jets. The algorithm is based on application of the difference potentials method (DPM). Previously, similar boundary conditions have been implemented for calculation of external compressible viscous flows around finite bodies. The proposed modification substantially extends the applicability range of the DPM-based algorithm. We present the general formulation of the problem, describe our numerical methodology, and discuss the corresponding computational results. The particular configuration that we analyze is a slender three-dimensional body with boat-tail geometry and supersonic jet exhaust in a subsonic external flow under zero angle of attack. Similar to the results obtained earlier for the flows around airfoils and wings, current results for the jet flow case corroborate the superiority of the DPM-based ABCs over standard local methodologies from the standpoints of accuracy, overall numerical performance, and robustness DA - 2000/11// PY - 2000/11// DO - 10.2514/2.888 VL - 38 IS - 11 SP - 2014-2022 SN - 0001-1452 1533-385X UR - http://dx.doi.org/10.2514/2.888 ER - TY - CONF TI - A Two-Level Aggregation-Based {Newton-Krylov-Schwarz} Method for Hydrology AU - Jenkins, E W AU - Berger, R C AU - Hallberg, J P AU - Howington, Stacy E AU - Kelley, C T AU - Schmidt, Joseph H AU - Stagg, Alan AU - Tocci, M D A2 - Keyes, D E A2 - Ecer, A A2 - Periaux, J A2 - Satofuka, N C2 - 2000/// C3 - Parallel Computational Fluid Dynamics 1999 DA - 2000/// SP - 257-264 PB - North Holland ER - TY - CONF TI - Broyden Method AU - Kelley, C T A2 - Hazenwinkel, M C2 - 2000/// C3 - Encyclopedia of Mathematics: Supplement II CY - Dordrecht DA - 2000/// SP - 96-98 PB - Kluwer ER - TY - JOUR TI - Mesh Independence of Matrix-Free Methods for Path Following AU - Ferng, W R AU - Kelley, C T T2 - SIAM J. Sci. Comp. DA - 2000/// PY - 2000/// VL - 21 SP - 1835-1850 ER - TY - CONF TI - {Broyden-Fletcher-Goldfarb-Shanno} Method AU - Kelley, C T A2 - Hazenwinkel, M C2 - 2000/// C3 - Encyclopedia of Mathematics: Supplement II CY - Dordrecht DA - 2000/// SP - 95-96 PB - Kluwer ER - TY - RPRT TI - Transformation Approaches for Simulating Flow in Variably Saturated Porous Media AU - Miller, C T AU - Williams, G A AU - Kelley, C T A3 - North Carolina State University, Center for Research in Scientific Computation DA - 2000/1// PY - 2000/1// VL - 36 SP - 923-934 PB - North Carolina State University, Center for Research in Scientific Computation ER - TY - BOOK TI - Industrial Mathematics: The 1998 CRSC Workshop A3 - Gremaud, P.A. A3 - Li, Z. A3 - Smith, R. C. A3 - Tran, H.T. DA - 2000/// PY - 2000/// PB - SIAM SN - 0898714672 ER - TY - JOUR TI - Self-similar intermediate asymptotics for a degenerate parabolic filtration-absorption equation AU - Barenblatt, G. I. AU - Bertsch, M. AU - Chertock, A. E. AU - Prostokishin, V. M. T2 - Proceedings of the National Academy of Sciences AB - The equation partial differential(t)u = u partial differential(xx)(2)u -(c-1)( partial differential(x)u)(2) is known in literature as a qualitative mathematical model of some biological phenomena. Here this equation is derived as a model of the groundwater flow in a water-absorbing fissurized porous rock; therefore, we refer to this equation as a filtration-absorption equation. A family of self-similar solutions to this equation is constructed. Numerical investigation of the evolution of non-self-similar solutions to the Cauchy problems having compactly supported initial conditions is performed. Numerical experiments indicate that the self-similar solutions obtained represent intermediate asymptotics of a wider class of solutions when the influence of details of the initial conditions disappears but the solution is still far from the ultimate state: identical zero. An open problem caused by the nonuniqueness of the solution of the Cauchy problem is discussed. DA - 2000/8/29/ PY - 2000/8/29/ DO - 10.1073/pnas.97.18.9844 VL - 97 IS - 18 SP - 9844-9848 J2 - Proceedings of the National Academy of Sciences LA - en OP - SN - 0027-8424 1091-6490 UR - http://dx.doi.org/10.1073/pnas.97.18.9844 DB - Crossref ER - TY - JOUR TI - Strict Stability of High-Order Compact Implicit Finite-Difference Schemes: The Role of Boundary Conditions for Hyperbolic PDEs, I AU - Abarbanel, Saul S. AU - Chertock, Alina E. T2 - Journal of Computational Physics AB - Temporal, or “strict,” stability of approximation to PDEs is much more difficult to achieve than the “classical” Lax stability. In this paper, we present a class of finite-difference schemes for hyperbolic initial boundary value problems in one and two space dimensions that possess the property of strict stability. The approximations are constructed so that all eigenvalues of corresponding differentiation matrix have a nonpositive real part. Boundary conditions are imposed by using penalty-like terms. Fourth- and sixth-order compact implicit finite-difference schemes are constructed and analyzed. Computational efficacy of the approach is corroborated by a series of numerical tests in 1-D and 2-D scalar problems. DA - 2000/5// PY - 2000/5// DO - 10.1006/jcph.2000.6420 VL - 160 IS - 1 SP - 42-66 J2 - Journal of Computational Physics LA - en OP - SN - 0021-9991 UR - http://dx.doi.org/10.1006/jcph.2000.6420 DB - Crossref KW - hyperbolic PDEs KW - boundary conditions KW - stability KW - accuracy KW - error bounds ER - TY - JOUR TI - Strict Stability of High-Order Compact Implicit Finite-Difference Schemes: The Role of Boundary Conditions for Hyperbolic PDEs, II AU - Abarbanel, Saul S. AU - Chertock, Alina E. AU - Yefet, Amir T2 - Journal of Computational Physics AB - This paper deals with the problem of systems of hyperbolic PDEs in one and two space dimensions, using the theory of part I [7]. DA - 2000/5// PY - 2000/5// DO - 10.1006/jcph.2000.6421 VL - 160 IS - 1 SP - 67-87 J2 - Journal of Computational Physics LA - en OP - SN - 0021-9991 UR - http://dx.doi.org/10.1006/jcph.2000.6421 DB - Crossref KW - hyperbolic PDEs KW - boundary conditions KW - stability KW - accuracy KW - error bounds ER - TY - JOUR TI - Optimization of Automotive Valve Train Components with Implict Filtering AU - Choi, T.D. AU - Eslinger, O.J. AU - Kelley, C.T. AU - David, J.W. AU - Etheridge, M. T2 - Optimization and Engineering DA - 2000/// PY - 2000/// VL - 1 SP - 9–28 ER - TY - JOUR TI - Non-Reflecting Artificial Boundary Conditions for the Replacement of Truncated Equations with Lacunae AU - Ryaben’kii, V.S. AU - Turchaninov, V.I. AU - Tsynkov, S.V. T2 - Mathematical Modeling DA - 2000/// PY - 2000/// VL - 12 IS - 12 SP - 108–127 ER - TY - JOUR TI - Global artificial boundary conditions for computation of external flows with jets AU - Tsynkov, Semyon AU - Abarbanel, Saul AU - Nordstrom, Jan AU - Ryaben'kii, Victor AU - Vasta, Veer T2 - AIAA Journal DA - 2000/1// PY - 2000/1// DO - 10.2514/3.14645 VL - 38 SP - 2014-2022 J2 - AIAA Journal LA - en OP - SN - 0001-1452 1533-385X UR - http://dx.doi.org/10.2514/3.14645 DB - Crossref ER - TY - JOUR TI - Analysis and comparison of four anhysteretic polarization models for lead magnesium niobate AU - Piquette, JC AU - Smith, RC T2 - JOURNAL OF THE ACOUSTICAL SOCIETY OF AMERICA AB - Four anhysteretic polarization models that have been used in the literature to evaluate data acquired from lead magnesium niobate (PMN) are analyzed and compared. Derivations of two of the models from assumed spatial distributions of dipole energy states, using first physical principles, are presented. A third model is derived from a suitable integral averaging calculation. These derivations are used as the basis for developing an integral equation for determining an energy-state distribution that produces a fourth model, which was not originally formulated in terms of an assumed distribution. A new polarization function is also presented. Excellent approximations to each of the four polarization functions of interest can be deduced from this new polarization function by adjusting the numerical value of just a single parameter. An application of two of the models to data is presented. It is shown that it can be necessary to consider a sample to be an admixture of two distinct species of poles, in the sense that two polarization functions must be added together in order to accommodate the data. DA - 2000/10// PY - 2000/10// DO - 10.1121/1.1310670 VL - 108 IS - 4 SP - 1651-1662 SN - 0001-4966 ER - TY - JOUR TI - Approximation methods for inverse problems governed by nonlinear parabolic systems AU - Banks, HT AU - Musante, CJ AU - Raye, JK T2 - NUMERICAL FUNCTIONAL ANALYSIS AND OPTIMIZATION AB - Abstract We present a rigorous theoretical framework for approximation of nonlinear parabolic systems with delays in the context of inverse least squares problems. Convergence of approximate optimal parameters and that of forward solutions in the context of semidiscrete Galerkin schemes are given. Sample numerical results demonstrating the convergence are given for a model of dioxin uptake and elimination in a distributed liver model that is a special case of the general theoretical framework. Keywords: Inverse problemsnonlinear parabolic systemsapproximation techniquesleast squares optimizationcomputational methods *This research was supported in part by the Air Force Office of Scientific Research (AFOSR) under Grants F-49620-95-1-0236, F-49620-98-1-0180, F-49620-95-1-0375, and F-49620-93-1-0355 The research of CJM and JKR was funded by US Department of Education Graduate Assistance in Areas of National Need (GAANN) Fellowships under Grants P200A50075 and P200A70707, respectively. CJM also received support from the 1997 AFOSR Graduate Summer Research Program and the Armstrong Laboratory. Part of this research was carried out while HTB and CJM were visitors of the Institut Henri Poincare, Centre Emile Borel. † Author to whom correspondence should be addressed. ‡ Current address: U.S. Environmental Protection Agency, National Health and Environmental Effects Research Laboratory, Experimental Toxicology Division, Mail Drop 74, Research Triangle Park, NC 27711. *This research was supported in part by the Air Force Office of Scientific Research (AFOSR) under Grants F-49620-95-1-0236, F-49620-98-1-0180, F-49620-95-1-0375, and F-49620-93-1-0355 The research of CJM and JKR was funded by US Department of Education Graduate Assistance in Areas of National Need (GAANN) Fellowships under Grants P200A50075 and P200A70707, respectively. CJM also received support from the 1997 AFOSR Graduate Summer Research Program and the Armstrong Laboratory. Part of this research was carried out while HTB and CJM were visitors of the Institut Henri Poincare, Centre Emile Borel. † Author to whom correspondence should be addressed. ‡ Current address: U.S. Environmental Protection Agency, National Health and Environmental Effects Research Laboratory, Experimental Toxicology Division, Mail Drop 74, Research Triangle Park, NC 27711. Notes *This research was supported in part by the Air Force Office of Scientific Research (AFOSR) under Grants F-49620-95-1-0236, F-49620-98-1-0180, F-49620-95-1-0375, and F-49620-93-1-0355 The research of CJM and JKR was funded by US Department of Education Graduate Assistance in Areas of National Need (GAANN) Fellowships under Grants P200A50075 and P200A70707, respectively. CJM also received support from the 1997 AFOSR Graduate Summer Research Program and the Armstrong Laboratory. Part of this research was carried out while HTB and CJM were visitors of the Institut Henri Poincare, Centre Emile Borel. † Author to whom correspondence should be addressed. ‡ Current address: U.S. Environmental Protection Agency, National Health and Environmental Effects Research Laboratory, Experimental Toxicology Division, Mail Drop 74, Research Triangle Park, NC 27711. DA - 2000/// PY - 2000/// DO - 10.1080/01630560008816986 VL - 21 IS - 7-8 SP - 791-816 SN - 0163-0563 KW - inverse problems KW - nonlinear parabolic systems KW - approximation techniques KW - least squares optimization KW - computational methods ER - TY - JOUR TI - A domain wall model for hysteresis in piezoelectric materials AU - Smith, RC AU - Ounaies, Z T2 - JOURNAL OF INTELLIGENT MATERIAL SYSTEMS AND STRUCTURES DA - 2000/1// PY - 2000/1// DO - 10.1177/104538900772664413 VL - 11 IS - 1 SP - 62-79 SN - 1045-389X ER - TY - JOUR TI - A coupled structural-magnetic strain and stress model for magnetostrictive transducers AU - Dapino, M. J. AU - Smith, Ralph AU - Faidley, L. E. AU - Flatau, A. B. T2 - Journal of Intelligent Material Systems and Structures AB - This paper addresses the modeling of strains and forces generated by magnetostrictive transducers in response to applied magnetic fields. The magnetostrictive effect is modeled by considering both the rotation of magnetic moments in response to the field and the elastic vibrations in the transducer. The former is modeled with the Jiles-Atherton model of ferromagnetic hysteresis in combination with a quartic magnetostriction law. The latter is modeled through force balancing which yields a PDE system with magnetostrictive inputs and boundary conditions given by the specific transducer design. The solution to this system provides both rod displacements and forces. The calculated forces are used to quantify the magnetomechanical effect in the transducer core, i.e., the stress-induced magnetization changes. This is done by considering a “law of approach” to the anhysteretic magnetization. The resulting model provides a representation of the bidirectional coupling between the magnetic and elastic states. It is demonstrated that the model accurately characterizes the magnetic hysteresis in the material, as well as the strains and forces output by the transducer under conditions typical of engineering applications. DA - 2000/// PY - 2000/// DO - 10.1106/MJ6A-FBP9-9M61-0E1F VL - 11 IS - 2 SP - 135–152 ER - TY - JOUR TI - Feedback control methodologies for nonlinear systems AU - Beeler, SC AU - Tran, HT AU - Banks, HT T2 - JOURNAL OF OPTIMIZATION THEORY AND APPLICATIONS AB - A number of computational methods have been proposed in the literature to design and synthesize feedback controls when the plant is modeled by nonlinear dynamics. However, it is not immediately clear which is the best method for a given problem; this may depend on the nature of the nonlinearities, size of the system, whether the amount of control used or time needed for the method is a concern, and other factors. In this paper, a comprehensive comparison study of five methods for the synthesis of nonlinear control systems is carried out. The performance of the methods on several test problems are studied, and some recommendations are made as to which feedback control method is best to use under various conditions. DA - 2000/10// PY - 2000/10// DO - 10.1023/A:1004607114958 VL - 107 IS - 1 SP - 1-33 SN - 0022-3239 KW - nonlinear optimal feedback control KW - Hamilton-Jacobi-Bellman equation KW - state-dependent Riccati equation KW - interpolation of open-loop controls ER - TY - JOUR TI - Transformation approaches for simulating flow in variably saturated porous media AU - Williams, GA AU - Miller, CT AU - Kelley, CT T2 - WATER RESOURCES RESEARCH AB - Sharp fronts with rapid changes in fluid saturations over short distance and timescales often exist in multiphase flow in subsurface systems. Such highly nonlinear problems are notoriously difficult to solve, and standard solution approaches are often inefficient and unreliable. We summarize four existing and one new transformation method (IT2) for solving Richards'; equation within a common framework and compare performance for a range of medium properties and simulation conditions. The new IT2 transform is defined as a linear combination of volumetric water fraction of the aqueous phase and integrated hydraulic conductivity terms. We show that transformation methods can significantly improve solution efficiency and robustness compared to standard solution approaches; optimal transformation parameters depend upon auxiliary conditions, medium properties, and spatial and temporal discretization and are difficult to evaluate a priori; and IT2 compares favorably with existing transforms. DA - 2000/4// PY - 2000/4// DO - 10.1029/1999WR900349 VL - 36 IS - 4 SP - 923-934 SN - 0043-1397 ER - TY - JOUR TI - Stability of the human respiratory control system II. Analysis of a three-dimensional delay state-space model AU - Batzel, JJ AU - Tran, HT T2 - JOURNAL OF MATHEMATICAL BIOLOGY DA - 2000/7// PY - 2000/7// DO - 10.1007/s002850000045 VL - 41 IS - 1 SP - 80-102 SN - 0303-6812 KW - respiratory control models KW - time delay KW - delay dependent stability KW - instability KW - numerical simulations ER - TY - JOUR TI - Stability of the human respiratory control system I. Analysis of a two-dimensional delay state-space model AU - Batzel, JJ AU - Tran, HT T2 - JOURNAL OF MATHEMATICAL BIOLOGY DA - 2000/7// PY - 2000/7// DO - 10.1007/s002850000044 VL - 41 IS - 1 SP - 45-79 SN - 1432-1416 KW - respiratory control models KW - time delay KW - delay-dependent stability KW - instability KW - numerical simulations ER - TY - JOUR TI - Output regulation for linear distributed parameter systems AU - Byrnes, C. I. AU - Lauko, I. G. AU - Gilliam, D. S. AU - Shubov, V. I. T2 - IEEE Transactions on Automatic Control DA - 2000/// PY - 2000/// VL - 45 IS - 12 SP - 2236-2252 ER - TY - JOUR TI - Reduced order model compensator control of species transport in a CVD reactor AU - Kepler, GM AU - Tran, HT AU - Banks, HT T2 - OPTIMAL CONTROL APPLICATIONS & METHODS AB - We propose the use of proper orthogonal decomposition (POD) techniques as a reduced basis method for computation of feedback controls and compensators in a high-pressure chemical vapour deposition (HPCVD) reactor. In this paper, we present a proof-of-concept computational implementation of this method with a simplified growth example for III–V layers in which we implement Dirichlet boundary control of a dilute Group III reactant transported by convection and diffusion to an absorbing substrate with no reactions. We implement the model-based feedback control using a reduced order state estimator based on observations of the flux of reactant at the substrate centre. This is precisely the type of measurements available with current sensing technology. We demonstrate that the reduced order state estimator or compensator system is capable of substantial control authority when applied to a high-order system. In principle, these ideas can be extended to more general HPCVD control situations by including multiple species with gas-phase reactions and surface reactions. Copyright © 2000 John Wiley & Sons, Ltd. DA - 2000/// PY - 2000/// DO - 10.1002/1099-1514(200007/08)21:4<143::AID-OCA671>3.0.CO;2-Y VL - 21 IS - 4 SP - 143-160 SN - 0143-2087 KW - linear quadratic control KW - proper orthogonal decomposition KW - reduced order model KW - chemical vapour deposition KW - Dirichlet boundary control ER - TY - JOUR TI - Modeling instability in the control system for human respiration: applications to infant non-REM sleep AU - Batzel, JJ AU - Tran, HT T2 - APPLIED MATHEMATICS AND COMPUTATION AB - Mathematical models of the human respiratory control system have been developed since 1940 to study a wide range of features of this complex system. The phenomena collectively referred to as periodic breathing (including Cheyne–Stokes respiration and apneustic breathing) have important medical implications. The hypothesis that periodic breathing is the result of delay in the feedback signals to the respiratory control system has been studied since the work of F.S. Grodins, J. Gray, A.I. Norins, R.W. Jones [J. Appl. Physiol. 1 (1954) 283–308] in the early 1950s. The purpose of this paper is to extend the model presented by M.C.K. Khoo, R.E. Kronauer, K.P. Strohl, A.S. Slutsky [J. Appl. Physiol. 53 (3) (1982) 644–659] in 1991 to include variable delay in the feedback control loop and to study the phenomena of periodic breathing and apnea as they occur during quiet sleep in infant sleep respiration at around 4 months of age. The nonlinear mathematical model consists of a feedback control system of five delay differential equations. Numerical simulations are performed to study instabilities in the control system and the occurrence of periodic breathing and apnea in the above case which is a time frame of high incidence of sudden infant death syndrome (SIDS). DA - 2000/4/1/ PY - 2000/4/1/ DO - 10.1016/s0096-3003(99)00112-5 VL - 110 IS - 1 SP - 1-51 SN - 0096-3003 ER - TY - JOUR TI - Energy-based hysteresis model for magnetostrictive transducers AU - Calkins, FT AU - Smith, RC AU - Flatau, AB T2 - IEEE TRANSACTIONS ON MAGNETICS AB - This paper addresses the modeling of hysteresis in magnetostrictive transducers in the context of control applications that require an accurate characterization of the relation between input currents and strains output by the transducer. This relation typically exhibits significant nonlinearities and hysteresis because of inherent properties of magnetostrictive materials. The characterization considered here is based on the Jiles-Atherton mean field model for ferromagnetic hysteresis in combination with a quadratic moment rotation model for magnetostriction. As demonstrated by comparison with experimental data, the magnetization model very adequately quantifies both major and minor loops under various operating conditions. The combined model can then be used to accurately characterize output strains at moderate drive levels. The advantages of this model lie in the small number (six) of required parameters and its flexibility under a variety of operating conditions. DA - 2000/3// PY - 2000/3// DO - 10.1109/20.825804 VL - 36 IS - 2 SP - 429-439 SN - 0018-9464 KW - hysteresis model KW - magnetorestrictive transducer ER - TY - JOUR TI - Superlinear convergence and implicit filtering AU - Choi, TD AU - Kelley, CT T2 - SIAM JOURNAL ON OPTIMIZATION AB - In this paper we show how the implicit filtering algorithm can be coupled with the BFGS quasi-Newton update to obtain a superlinearly convergent iteration if the noise in the objective function decays sufficiently rapidly as the optimal point is approached. In this way we give insight into the observations of good performance in practice of quasi-Newton methods when they are coupled with implicit filtering. We also report on numerical experiments that show how an implementation of implicit filtering that exploits these new results can improve the performance of the algorithm. DA - 2000/6/18/ PY - 2000/6/18/ DO - 10.1137/S1052623499354096 VL - 10 IS - 4 SP - 1149-1162 SN - 1052-6234 KW - noisy optimization KW - implicit filtering KW - BFGS algorithm KW - superlinear convergence ER - TY - JOUR TI - Reduced-order model feedback control design: Numerical implementation in a thin shell model AU - Banks, HT AU - Rosario, RCH AU - Smith, RC T2 - IEEE TRANSACTIONS ON AUTOMATIC CONTROL AB - Reduced-order models employing the Lagrange and popular proper orthogonal decomposition (POD) reduced-basis methods in numerical approximation and feedback control of systems are presented and numerically tested. The system under consideration is a thin cylindrical shell with surface-mounted piezoceramic actuators. Donnell-Mushtari equations, modified to include Kelvin-Voigt damping, are used to model the system dynamics. Basis functions constructed from Fourier polynomials tensored with cubic splines are employed in the Galerkin expansion of the full-order model. Reduced-basis elements are then formed from full order approximations of the exogenously excited shell taken at different time instances. Numerical examples illustrating the features of the reduced-basis methods are presented. As a first step toward investigating the behavior of the methods when implemented in physical systems, the use of reduced-order model feedback control gains in the full order model is considered and numerical examples are presented. DA - 2000/7// PY - 2000/7// DO - 10.1109/9.867024 VL - 45 IS - 7 SP - 1312-1324 SN - 0018-9286 KW - LQR feedback control KW - proper orthogonal decomposition KW - reduced-basis computational methods KW - thin shell dynamics ER - TY - JOUR TI - Nondestructive evaluation using a reduced-order computational methodology AU - Banks, HT AU - Joyner, ML AU - Wincheski, B AU - Winfree, WP T2 - INVERSE PROBLEMS AB - This paper uses eddy current based techniques and reduced-order modelling to explore the feasibility of detecting subsurface damage in structures such as air foils and pipelines. To identify the geometry of the damage, an optimization algorithm is employed which requires solving the forward problem numerous times. To implement these methods in a practical setting, the forward algorithm must be solved with extremely fast and accurate solution methods. Therefore, our computational methods are based on the reduced-order Karhunen-Loeve or proper orthogonal decomposition techniques. For proof of concept, we implement the methodology on a 2D problem and find the methods to be efficient and robust even with data containing 10% relative noise. Furthermore, the methods are fast: our findings suggest we can reduce the computational time on average by a factor of 3000. DA - 2000/8// PY - 2000/8// DO - 10.1088/0266-5611/16/4/304 VL - 16 IS - 4 SP - 929-945 SN - 0266-5611 ER - TY - JOUR TI - Structural magnetic strain model for magnetostrictive transducers AU - Dapino, MJ AU - Smith, RC AU - Flatau, AB T2 - IEEE TRANSACTIONS ON MAGNETICS AB - This paper addresses the modeling of strains generated by magnetostrictive transducers in response to applied magnetic fields. The measured strains depend on both the rotation of moments within the material in response to the field and the elastic properties of the material. The magnetic behavior is characterized by considering the Jiles-Atherton mean field theory for ferromagnetic hysteresis in combination with a quadratic moment rotation model for magnetostriction. Elastic properties must be incorporated to account for the dynamics of the material as it vibrates. This is modeled by force balancing, which yields a wave equation with magnetostrictive inputs. The validity of the resulting transducer model is illustrated by comparison with experimental data. DA - 2000/5// PY - 2000/5// DO - 10.1109/20.846217 VL - 36 IS - 3 SP - 545-556 SN - 0018-9464 KW - hysteresis KW - magnetomechanical model KW - magnetostrictive transducer ER - TY - JOUR TI - Time and frequency domain scattering for the one-dimensional wave equation AU - Browning, BL T2 - INVERSE PROBLEMS AB - We give a constructive method for extending time domain data for the inverse scattering problem for the one-dimensional wave equation. We show that a reflection operator on L2(-T,T) with T finite is essentially a Hankel operator and then modify the Nehari extension of the kernel of the reflection operator to obtain a reflection operator on L2() that is consistent with conservation of energy. This extension result allows frequency domain techniques to be used when the time domain data are only available for finite time, and we demonstrate this by using the frequency domain characterization of reflection coefficients to obtain a new proof of the characterization of reflection operators on L2(-T,T). We also give an a priori estimate for the operator norm of the reflection operator on L2(-T,T) and use the theory of Toeplitz operators to show how the singular values of these reflection operators are related to the reflection coefficient. DA - 2000/10// PY - 2000/10// DO - 10.1088/0266-5611/16/5/315 VL - 16 IS - 5 SP - 1377-1403 SN - 0266-5611 ER - TY - JOUR TI - Optimized design of switching amplifiers for piezoelectric actuators AU - Chandrasekaran, S AU - Lindner, DK AU - Smith, RC T2 - JOURNAL OF INTELLIGENT MATERIAL SYSTEMS AND STRUCTURES AB - The formulation and solution of an optimization problem for the design of a current controlled switching power amplifier to drive a piezoelectric actuator is the subject of this paper. The design is formulated as a continuous optimization problem. A detailed model that includes the anhysteretic nonlinearity between the electric field and polarization is developed and is coupled with a dynamic model of the amplifier. The design specifications are formulated as optimization constraints. The objective function is chosen to be the weight of the inductor. Optimization results are presented to demonstrate the efficiency of the proposed design methodology. DA - 2000/11// PY - 2000/11// DO - 10.1106/XFC7-PD82-LDFC-T2R9 VL - 11 IS - 11 SP - 887-901 SN - 1045-389X ER - TY - JOUR TI - Mesh independence of matrix-free methods for path following AU - Ferng, WR AU - Kelley, CT T2 - SIAM JOURNAL ON SCIENTIFIC COMPUTING AB - In this paper we consider a matrix-free path following algorithm for nonlinear parameter-dependent compact fixed point problems. We show that if these problems are discretized so that certain collective compactness and strong convergence properties hold, then this algorithm can follow smooth folds and capture simple bifurcations in a mesh-independent way. DA - 2000/5/21/ PY - 2000/5/21/ DO - 10.1137/S1064827598339360 VL - 21 IS - 5 SP - 1835-1850 SN - 1064-8275 KW - path following KW - bifurcation KW - collective compactness KW - fold point KW - mesh independence KW - matrix-free method KW - GMRES KW - Arnoldi method KW - singularity ER -