Parallel preconditioners for solutions of dense linear systems with tens of millions of unknowns

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2007-11-09

Author

Malas, Tahir
Ergül, Özgür Salih
Gurel, Levent

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This work is licensed under a Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 International License.

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We propose novel parallel preconditioning schemes for the iterative solution of integral equation methods. In particular, we try to improve convergence rate of the ill-conditioned linear systems formulated by the electric-field integral equation, which is the only integral-equation formulation for targets having open surfaces. For moderate-size problems, iterative solution of the neat-field system enables much faster convergence compared to the widely used sparse approximate inverse preconditioner. For larger systems, 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, which are the largest problems ever reported in computational electromagnetics.

Subject Keywords

Data structures, Computational complexity, Geometry, Noise measurement, Iterative methods, Sparse matrices, Computational electromagnetics, MLFMA, Integral equations, Linear systems

URI

https://hdl.handle.net/11511/47290

DOI

https://doi.org/10.1109/iscis.2007.4456895

Collections

Department of Electrical and Electronics Engineering, Conference / Seminar

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Citation Formats

T. Malas, Ö. S. Ergül, and L. Gurel, “Parallel preconditioners for solutions of dense linear systems with tens of millions of unknowns,” 2007, Accessed: 00, 2020. [Online]. Available: https://hdl.handle.net/11511/47290.