Effective preconditioners for large integral-equation problems

Date
2007-11
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Source Title
IET Seminar Digest
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Publisher
IET
Volume
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Pages
1 - 5
Language
English
Type
Conference Paper
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Abstract

We consider effective preconditioning schemes for the iterative solution of integral-equation methods. For parallel implementations, the sparse approximate inverse or the iterative solution of the near-field system enables fast convergence up to certain problem sizes. However, for very large problems, the near-field matrix itself becomes too crude approximation to the dense system matrix and preconditioners generated from the near-field interactions cannot be effective. Therefore, we propose an approximation strategy to the multilevel fast multipole algorithm (MLFMA) to be used as a preconditioner. Our numerical experiments reveal that this scheme significantly outperforms other preconditioners. With the combined effort of effective preconditioners and an efficiently parallelized MLFMA, we are able to solve targets with tens of millions of unknowns in a few hours.

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Keywords
Integral equation methods, Large-scale problems, Preconditioning, electromagnetic scattering, Crude approximations, Dense systems, Fast convergence, Iterative solutions, Matrix, Multilevel fast multipole algorithms, Near field interactions, Near-field, Numerical experiments, Parallel implementations, Preconditioners, Preconditioning, electromagnetic scattering, Problem size, Sparse approximate inverse, Antennas, Approximation algorithms, Boundary element method, Electromagnetic wave scattering, Integral equations, Radar antennas
Citation
Published Version (Please cite this version)