Solutions of large integral-equation problems with preconditioned MLFMA
Author
Ergül, Özgür
Malas, Tahir
Ünal, Alper
Gürel, Levent
Date
2007Source Title
Proceedings of the 37th European Microwave Conference, EuMA 2007
Publisher
IEEE
Pages
166 - 169
Language
English
Type
Conference PaperItem Usage Stats
84
views
views
49
downloads
downloads
Metadata
Show full item recordAbstract
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.
Keywords
Computational geometryElectromagnetic 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