Iterative solution of Maxwell's equations in frequency domain

We have developed an iterative solver for the Moment Method. It computes a matrix–vector product with the multilevel Fast Multipole Method, which makes the method scale with the number of unknowns. ...

[1]  R. Coifman,et al.  The fast multipole method for the wave equation: a pedestrian prescription , 1993, IEEE Antennas and Propagation Magazine.

[2]  Efstratios Gallopoulos,et al.  Iterative methods for complex symmetric systems with multiple right-hand sides , 1994 .

[3]  J. Nédélec.  Acoustic and electromagnetic equations , 2001 .

[4]  Stephen A. Vavasis,et al.  Preconditioning for Boundary Integral Equations , 1992, SIAM J. Matrix Anal. Appl..

[5]  Valeria Simoncini.  A Stabilized QMR Version of Block BiCG , 1997 .

[6]  Martin Nilsson.  A fast multipole method solver for large scale scattering problems , 2001 .

[7]  Martin Nilsson,et al.  Solving the Electric Field Integral Equation using a Sparse Approximate Inverse preconditioned iterative method , 1999 .

[8]  Johan Bengtsson,et al.  Efficient symbolic state exploration of timed systems : Theory and implementation , 2001 .

[9]  Fredrik Edelvik.  Finite volume solvers for the Maxwell equations in time domain , 2000 .

[10]  G. Arfken.  Mathematical Methods for Physicists , 1967 .

[11]  Roland W. Freund,et al.  An Implementation of the QMR Method Based on Coupled Two-Term Recurrences , 1994, SIAM J. Sci. Comput..

[12]  M'Barek Fares,et al.  A boundary-element solution of the Leontovitch problem , 1999 .

[13]  Eva Mossberg.  Higher order finite difference methods for wave propagation problems , 2002 .

[14]  R. Freund,et al.  Iterative solution of multiple radiation and scattering problems in structural acoustics using a block quasi-minimal residual algorithm , 1997 .

[15]  Jiming Song,et al.  Multilevel fast‐multipole algorithm for solving combined field integral equations of electromagnetic scattering , 1995 .

[16]  R. Kouyoumjian,et al.  A uniform geometrical theory of diffraction for an edge in a perfectly conducting surface , 1974 .

[17]  Fredrik Edelvik,et al.  A comparison of time‐domain hybrid solvers for complex scattering problems , 2002 .

[18]  V. H. Rumsey,et al.  Reaction Concept in Electromagnetic Theory , 1954 .

[19]  Allen Taflove,et al.  Computational Electrodynamics the Finite-Difference Time-Domain Method , 1995 .

[20]  Marcus J. Grote,et al.  Parallel Preconditioning with Sparse Approximate Inverses , 1997, SIAM J. Sci. Comput..

[21]  Richard Barrett,et al.  Templates for the Solution of Linear Systems: Building Blocks for Iterative Methods , 1994, Other Titles in Applied Mathematics.

[22]  D. J. Riley,et al.  VOLMAX: a solid-model-based, transient volumetric Maxwell solver using hybrid grids , 1997 .

[23]  Jian-Ming Jin,et al.  Fast and Efficient Algorithms in Computational Electromagnetics , 2001 .

[24]  M. Nilsson.  A fast multipole accelerated block quasi minimum residual method for solving scattering from perfectly conducting bodies , 2000, IEEE Antennas and Propagation Society International Symposium. Transmitting Waves of Progress to the Next Millennium. 2000 Digest. Held in conjunction with: USNC/URSI National Radio Science Meeting (C.

[25]  Anne Greenbaum,et al.  Iterative methods for solving linear systems , 1997, Frontiers in applied mathematics.

[26]  Michael S. Warren,et al.  A portable parallel particle program , 1995 .

[27]  Stefan Söderberg.  A parallel block-based PDE solver with space-time adaptivity , 2001 .

[28]  R. Kleinman,et al.  Mathematical foundations for error estimation in numerical solutions of integral equations in electromagnetics , 1997 .

[29]  Johan Edlund,et al.  A parallel, iterative method of moments and physical optics hybrid solver for arbitrary surfaces , 2001 .

[30]  D. Wilton,et al.  Electromagnetic scattering by surfaces of arbitrary shape , 1980 .

[31]  W. Chew,et al.  Approximate inverse preconditioner for near resonant scattering problems , 1998, IEEE Antennas and Propagation Society International Symposium. 1998 Digest. Antennas: Gateways to the Global Network. Held in conjunction with: USNC/URSI National Radio Science Meeting (Cat. No.98CH36.

[32]  Eric F Darve.  The Fast Multipole Method , 2000 .

[33]  Guillaume Alléon,et al.  Sparse approximate inverse preconditioning for dense linear systems arising in computational electromagnetics , 1997, Numerical Algorithms.

[34]  V. Rokhlin.  Diagonal Forms of Translation Operators for the Helmholtz Equation in Three Dimensions , 1993 .

[35]  Stefan A. SauterLehrstuhl.  Eecient Automatic Quadrature in 3{d Galerkin Bem , 1996 .

[36]  Carretera de Valencia,et al.  The finite element method in electromagnetics , 2000 .