NDLI: Incomplete LU Preconditioning with the Multilevel Fast Multipole Algorithm for Electromagnetic Scattering

Content Provider	Society for Industrial and Applied Mathematics (SIAM)
Author	Grel, Levent Malas, Tahr
Copyright Year	2007
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 ${\cal O}(n\log n)$ complexity of MLFMA. We conclude that the no-fill ILU(0) 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.
Starting Page	1476
Ending Page	1494
Page Count	19
File Format	PDF
ISSN	10648275
DOI	10.1137/060659107
e-ISSN	10957197
Issue Number	4
Volume Number	29
Language	English
Publisher	Society for Industrial and Applied Mathematics
Publisher Date	2007-06-21
Access Restriction	Subscribed
Subject Keyword	Diffraction, scattering Iterative methods for linear systems multilevel fast multipole algorithm Integral representations, integral operators, integral equations methods incomplete LU preconditioners Method of moments preconditioning electromagnetic scattering
Content Type	Text
Resource Type	Article
Subject	Applied Mathematics Computational Mathematics

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