Incomplete LU preconditioning with the multilevel fast multipole algorithm for electromagnetic scattering
Date
2007Source Title
SIAM Journal on Scientific Computing
Print ISSN
1064-8275
Electronic ISSN
1095-7197
Publisher
Society for Industrial and Applied Mathematics
Volume
29
Issue
4
Pages
1476 - 1494
Language
English
Type
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Abstract
Iterative solution of large-scale scattering problems in computational electromagnetics with the multilevel fast multipole algorithm (MLFMA) requires strong preconditioners, especially for the electric-field integral equation (EFIE) formulation. Incomplete LU (ILU) preconditioners are widely used and available in several solver packages. However, they lack robustness due to potential instability problems. In this study, we consider various ILU-class preconditioners and investigate the parameters that render them safely applicable to common surface integral formulations without increasing the script O sign(n log n) complexity of MLFMA. We conclude that the no-fill ILU(O) preconditioner is an optimal choice for the combined-field integral equation (CFIE). For EFIE, we establish the need to resort to methods depending on drop tolerance and apply pivoting for problems with high condition estimate. We propose a strategy for the selection of the parameters so that the preconditioner can be used as a black-box method. Robustness and efficiency of the employed preconditioners are demonstrated over several test problems.
Keywords
Incomplete LU preconditionersMultilevel fast multipole algorithm
Electromagnetic scattering