Solutions of large integral-equation problems with preconditioned MLFMA

Date
2007
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Source Title
Proceedings of the 37th European Microwave Conference, EuMA 2007
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Publisher
IEEE
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Pages
166 - 169
Language
English
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Conference Paper
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Abstract

We report the solution of the largest integral-equation problems in computational electromagnetics. We consider matrix equations obtained from the discretization of the integral-equation formulations that are solved iteratively by employing parallel multilevel fast multipole algorithm (MLFMA). With the efficient parallelization of MLFMA, scattering and radiation problems with millions of unknowns are easily solved on relatively inexpensive computational platforms. For the iterative solutions of the matrix equations, we are able to obtain accelerated convergence even for ill-conditioned matrix equations using advanced preconditioning schemes, such as nested preconditioned based on an approximate MLFMA. By orchestrating these diverse activities, we have been able to solve a closed geometry formulated with the CFIE containing 33 millions of unknowns and an open geometry formulated with the EFIE containing 12 millions of unknowns, which are the largest problems of their classes, to the best of our knowledge.

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Computational geometry, Electromagnetic wave scattering, Electromagnetism, Integral equations, Materials science, Microwaves, Numerical analysis, Parallel algorithms, Scattering, Electromagnetic scattering, Metamaterials, Multilevel fast multipole algorithm, Parallelization, Preconditioning techniques, Surface integral equations, Iterative methods
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Published Version (Please cite this version)