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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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
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Abstract	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.
AbstractList	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.
Author	Adelman, Ross Duraiswami, Ramani Gumerov, Nail A.
Author_xml	– sequence: 1 givenname: Ross surname: Adelman fullname: Adelman, Ross email: ross.n.adelman.civ@mail.mil organization: Army Res. Lab., Adelphi, MD, USA – sequence: 2 givenname: Nail A. surname: Gumerov fullname: Gumerov, Nail A. organization: Inst. for Adv. Comput. Studies, Univ. of Maryland, College Park, MD, USA – sequence: 3 givenname: Ramani surname: Duraiswami fullname: Duraiswami, Ramani organization: Inst. for Adv. Comput. Studies, Univ. of Maryland, College Park, MD, USA
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SubjectTerms	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
Title	FMM/GPU-Accelerated Boundary Element Method for Computational Magnetics and Electrostatics
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