Incomplete LU Preconditioning with the Multilevel Fast Multipole Algorithm for Electromagnetic Scattering
Incomplete LU Preconditioning with the Multilevel Fast Multipole Algorithm for Electromagnetic Scattering
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DOI：
10.1137/060659107
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发表时间：
2007-06
期刊：
影响因子：
--
通讯作者：
T. Malas;L. Gürel
中科院分区：
文献类型：
--
作者：
T. Malas;L. Gürel
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.
