An efficient sparse approximate inverse preconditioning for FMM implementation

Abstract

For efficiently solving large dense complex linear systems that arise in electric field integral equations (EFIE) of electromagnetic scattering problems, the fast multipole method (FMM) is used to accelerate the matrix‐vector product operations, and the sparse approximate inverse (SAI) preconditioning technique is employed to speed up the convergence rate of the Krylov iterations. A good quality SAI preconditioner in the FMM context is constructed based on the near‐field matrix of the EFIE. The main purpose of this paper is to show that the quality of the SAI preconditioner can be greatly improved by use of information from FMM implementation. Numerical experiments indicate that the resulted SAI preconditioner is very effective with FMM and can reduce the overall simulation time significantly. © 2007 Wiley Periodicals, Inc. Microwave Opt Technol Lett 49: 1746–1750, 2007; Published online in Wiley InterScience (www.interscience.wiley.com). DOI 10.1002/mop.22538

Schwarz-Krylov Subspace Method for MLFMM Analysis of Electromagnetic Wave Scattering Problems

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Geometry Based Preconditioner for Radiation Problems Involving Wire and Surface Basis Functions

“…Some of the most common techniques are those based on the sparse approximate inverse (SAI) preconditioning [10][11][12] and the incomplete LU (ILU) factorization type preconditioning [8,13,14].…”

An Efficient Sai Preconditioning Technique for Higher Order Hierarchical MLFMM Implementation

“…Usually the "reduced" least-squares problems (25) have much smaller size than that of least-squares problems (24). In MLFMM, N higher order hierarchical basis fuctions are divided into R groups, denoted by G p (p = 1, 2, .…”

“…The performance of SAI preconditioner is greatly influenced by the way of choosing nonzero pattern and the way of solving the least-squares problems in the minimization process. In this paper, information from higher order hierarchical MLFMM implementation is employed to develop a high quality SAI preconditioner, resulting in a faster convergence rate [24]. This paper is outlined as follows.…”