Incomplete LU Preconditioning with the Multilevel Fast Multipole Algorithm for Electromagnetic Scattering | Zendy

Tahir Malas | Zendy; Levent Gürel | Zendy

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

Author(s) -

Tahir Malas,

Levent Gürel

Publication year - 2007

Publication title -

siam journal on scientific computing

Language(s) - English

Resource type - Journals

SCImago Journal Rank - 1.674

H-Index - 147

eISSN - 1095-7197

pISSN - 1064-8275

DOI - 10.1137/060659107

Subject(s) - preconditioner , solver , integral equation , robustness (evolution) , fast multipole method , mathematics , electric field integral equation , computational electromagnetics , multipole expansion , electromagnetics , iterative method , algorithm , mathematical optimization , mathematical analysis , electromagnetic field , physics , quantum mechanics , electronic engineering , biochemistry , chemistry , engineering , gene

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. © 2007 Society for Industrial and Applied Mathematics

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