A fast frequency sweep approach using Padé approximations for solving Helmholtz finite element models

[1]  Miguel C. Junger,et al.  Sound, Structures, and Their Interaction , 1972 .

[2]  Lawrence T. Pileggi,et al.  Asymptotic waveform evaluation for timing analysis , 1990, IEEE Trans. Comput. Aided Des. Integr. Circuits Syst..

[3]  E. Grimme,et al.  Pade approximation of large-scale dynamic systems with Lanczos methods , 1994, Proceedings of 1994 33rd IEEE Conference on Decision and Control.

[4]  Jean-Pierre Berenger,et al.  A perfectly matched layer for the absorption of electromagnetic waves , 1994 .

[5]  Roland W. Freund,et al.  Efficient linear circuit analysis by Pade´ approximation via the Lanczos process , 1994, EURO-DAC '94.

[6]  John L. Volakis,et al.  AWE implementation for electromagnetic FEM analysis , 1996 .

[7]  F. Ihlenburg.  Finite Element Analysis of Acoustic Scattering , 1998 .

[8]  P. Monk,et al.  Optimizing the Perfectly Matched Layer , 1998 .

[9]  E. Turkel,et al.  Absorbing PML boundary layers for wave-like equations , 1998 .

[10]  Patrick R. Amestoy,et al.  Multifrontal parallel distributed symmetric and unsymmetric solvers , 2000 .

[11]  Raj Mittra,et al.  Finite element solution of electromagnetic problems over a wide frequency range via the Padé approximation , 1999 .

[12]  Michel Rochette,et al.  Calculation of vibro-acoustic frequency response functions using a single frequency boundary element solution and a Pade expansion , 1999 .

[13]  Roland W. Freund,et al.  A Lanczos-type method for multiple starting vectors , 2000, Math. Comput..

[14]  Madhujit Mukhopadhyay.  Vibrations, dynamics and structural systems , 2000 .

[15]  Jin-Fa Lee,et al.  Multipoint Galerkin asymptotic waveform evaluation for model order reduction of frequency domain FEM electromagnetic radiation problems , 2001 .

[16]  Matti Lassas,et al.  Analysis of the PML equations in general convex geometry , 2001, Proceedings of the Royal Society of Edinburgh: Section A Mathematics.

[17]  R. D. Slone,et al.  Fast frequency sweep model order reduction of polynomial matrix equations resulting from finite element discretizations , 2002 .

[18]  Jin-Fa Lee,et al.  Well-conditioned asymptotic waveform evaluation for finite elements , 2003 .

[19]  P. Pinsky,et al.  A Krylov subspace projection method for simultaneous solution of Helmholtz problems at multiple frequencies , 2003 .

[20]  P. Pinsky,et al.  Application of Padé via Lanczos approximations for efficient multifrequency solution of Helmholtz problems. , 2003, The Journal of the Acoustical Society of America.

[21]  B. Lohmann,et al.  Structure Preserving Order Reduction of Large Scale Second Order Systems , 2004 .

[22]  Xuan Zeng,et al.  SAPOR: second-order Arnoldi method for passive order reduction of RCS circuits , 2004, ICCAD 2004.

[23]  Zhaojun Bai,et al.  Arnoldi methods for structure-preserving dimension reduction of second-order dynamical systems , 2005 .

[24]  B. Lohmann,et al.  Reduction of second order systems using second order Krylov subspaces , 2005 .

[25]  Zhaojun Bai,et al.  SOAR: A Second-order Arnoldi Method for the Solution of the Quadratic Eigenvalue Problem , 2005, SIAM J. Matrix Anal. Appl..

[26]  P. Dooren,et al.  Model reduction of second order systems , 2005 .

[27]  Zhaojun Bai,et al.  Dimension Reduction of Large-Scale Second-Order Dynamical Systems via a Second-Order Arnoldi Method , 2005, SIAM J. Sci. Comput..

[28]  Frank Schmidt,et al.  A new finite element realization of the perfectly matched layer method for Helmholtz scattering problems on polygonal domains in two dimensions , 2006 .

[29]  B. Lohmann,et al.  Order reduction of large scale second-order systems using Krylov subspace methods , 2006 .

[30]  Mustafa Kuzuoglu,et al.  Near-field performance analysis of locally-conformal perfectly matched absorbers via Monte Carlo simulations , 2007, J. Comput. Phys..

[31]  Charbel Farhat,et al.  Fast frequency sweep computations using a multi‐point Padé‐based reconstruction method and an efficient iterative solver , 2007 .

[32]  Alfredo Bermúdez,et al.  An optimal perfectly matched layer with unbounded absorbing function for time-harmonic acoustic scattering problems , 2007, J. Comput. Phys..

[33]  M. Kuzuoglu,et al.  Non-Maxwellian Locally-Conformal PML Absorbers for Finite Element Mesh Truncation , 2007, IEEE Transactions on Antennas and Propagation.

[34]  Serkan Gugercin,et al.  H2 Model Reduction for Large-Scale Linear Dynamical Systems , 2008, SIAM J. Matrix Anal. Appl..

[35]  James P. Tuck-Lee,et al.  Adaptive frequency windowing for multifrequency solutions in structural acoustics based on the matrix Padé‐via‐Lanczos algorithm , 2008 .

[36]  Karl Meerbergen,et al.  Fast frequency response computation for Rayleigh damping , 2008 .

[37]  R. S. Puri,et al.  Reduced order fully coupled structural–acoustic analysis via implicit moment matching , 2009 .

[38]  Zhongxiao Jia,et al.  A Refined Second-order Arnoldi (RSOAR) Method for the Quadratic Eigenvalue Problem and Implicit Restarting , 2010 .

[39]  Peter M. Pinsky,et al.  Matrix‐Padé via Lanczos solutions for vibrations of fluid–structure interaction , 2010 .

[40]  Lloyd N. Trefethen,et al.  Impossibility of Fast Stable Approximation of Analytic Functions from Equispaced Samples , 2011, SIAM Rev..

[41]  Stijn Donders,et al.  On the use of model order reduction for acoustics: second-order Arnoldi and the adaptive windowing algorithm , 2011 .