Preconditioned, Adaptive, Multipole-Accelerated Iterative Methods for Three-Dimensional First-Kind Integral Equations of Potential Theory

This paper presents a preconditioned, Krylov-subspace iterative algorithm, where a modified multipole algorithm with a novel adaptation scheme is used to compute the iterates for solving dense matrix problems generated by Galerkin or collocation schemes applied to three-dimensional, first-kind, inte...

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Bibliographic Details
Published inSIAM journal on scientific computing Vol. 15; no. 3; pp. 713 - 735
Main Authors Nabors, K., Korsmeyer, F. T., Leighton, F. T., White, J.
Format Journal Article
LanguageEnglish
Published Philadelphia Society for Industrial and Applied Mathematics 01.05.1994
Subjects
Adaptation
Algorithms
Approximation
Charged particles
Computer engineering
Designers
Integral equations
Iterative methods
Methods
Microelectromechanical systems
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Summary:This paper presents a preconditioned, Krylov-subspace iterative algorithm, where a modified multipole algorithm with a novel adaptation scheme is used to compute the iterates for solving dense matrix problems generated by Galerkin or collocation schemes applied to three-dimensional, first-kind, integral equations that arise in potential theory. A proof is given that this adaptive algorithm reduces both matrix-vector product computation time and storage to order $N$, and experimental evidence is given to demonstrate that the combined preconditioned, adaptive, multipole-accelerated (PAMA) method is nearly order $N$ in practice. Examples from engineering applications are given to demonstrate that the accelerated method is substantially faster than standard algorithms on practical problems.
ISSN:1064-8275
1095-7197
DOI:10.1137/0915046