FMM/GPU-Accelerated Boundary Element Method for Computational Magnetics and Electrostatics

A fast multipole method (FMM)/graphics processing unit-accelerated boundary element method (BEM) for computational magnetics and electrostatics via the Laplace equation is presented. The BEM is an integral method, but the FMM is typically designed around monopole and dipole sources. To apply the FMM...

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Bibliographic Details
Published in:IEEE transactions on magnetics Vol. 53; no. 12; pp. 1 - 11
Main Authors: Adelman, Ross, Gumerov, Nail A., Duraiswami, Ramani
Format: Journal Article
Language:English
Published: New York IEEE 01.12.2017
The Institute of Electrical and Electronics Engineers, Inc. (IEEE)
Subjects:
Black boxes
Boundary element method
Boundary element methods
boundary integral equations
Computation
Data structures
Dipoles
Electrostatics
fast solvers
Galerkin method
Graphics processing units
Integral equations
Integrals
Laplace equation
Laplace equations
Magnetism
Mathematical analysis
Method of moments
Monopoles
Nonlinear programming
Parallel processing
parallel programming
ISSN:0018-9464, 1941-0069
Online Access:Get full text
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Summary:A fast multipole method (FMM)/graphics processing unit-accelerated boundary element method (BEM) for computational magnetics and electrostatics via the Laplace equation is presented. The BEM is an integral method, but the FMM is typically designed around monopole and dipole sources. To apply the FMM to the integral expressions in the BEM, the internal data structures and logic of the FMM must be changed. However, this can be difficult. For example, computing the multipole expansions due to the boundary elements requires computing single and double surface integrals over them. Moreover, FMM codes for monopole and dipole sources are widely available and highly optimized. This paper describes a method for applying the FMM unchanged to the integral expressions in the BEM. This method, called the correction factor matrix method, works by approximating the integrals using a quadrature. The quadrature points are treated as monopole and dipole sources, which can be plugged directly into current FMM codes. The FMM is effectively treated as a black box. Inaccuracies from the quadrature are corrected during a correction factor step. The method is derived, and example problems are presented showing accuracy and performance.
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ISSN:0018-9464
1941-0069
DOI:10.1109/TMAG.2017.2725951