Fast multipole method solution of three dimensional integral equation

J. M. Song; Weng Cho Chew

Fast multipole method solution of three dimensional integral equation

J. M. Song, Weng Cho Chew

Electrical and Computer Engineering

Research output: Contribution to journal › Conference article › peer-review

Abstract

The fast multipole method (FMM) speeds up the matrix-vector multiply in the conjugate gradient method when it is used to solve the matrix equation iteratively. In this paper, FMM is applied to solve the electromagnetic scattering from 3D arbitrary shape conducting bodies. The electric field integral equation (EFIE), magnetic field integral equation (MFIF), and combined field integral equation (CFIE) are considered. FMM formula for CFIE has been derived, which reduces the complexity of a matrix-vector multiply from O(N²) to O(N^1.5), where N is the number of unknowns. With a nonnested method, using the ray-propagation fast multipole algorithm, the cost of an FMM matrix vector multiply is reduced to O(N^4/3). A multilevel fast multipole algorithm (MLFMA) is implemented, whose complexity is further reduced to O(NlogN). The FMM also requires less memory, and hence, can solve a larger problem on a small computer.

Original language	English (US)
Pages (from-to)	1528-1531
Number of pages	4
Journal	IEEE Antennas and Propagation Society, AP-S International Symposium (Digest)
Volume	3
State	Published - Jan 1 1995
Event	Proceedings of the 1995 IEEE Antennas and Propagation Society International Symposium. Part 4 (of 4) - Newport Beach, CA, USA Duration: Jun 18 1995 → Jun 23 1995

ASJC Scopus subject areas

Electrical and Electronic Engineering

Cite this

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title = "Fast multipole method solution of three dimensional integral equation",

abstract = "The fast multipole method (FMM) speeds up the matrix-vector multiply in the conjugate gradient method when it is used to solve the matrix equation iteratively. In this paper, FMM is applied to solve the electromagnetic scattering from 3D arbitrary shape conducting bodies. The electric field integral equation (EFIE), magnetic field integral equation (MFIF), and combined field integral equation (CFIE) are considered. FMM formula for CFIE has been derived, which reduces the complexity of a matrix-vector multiply from O(N2) to O(N1.5), where N is the number of unknowns. With a nonnested method, using the ray-propagation fast multipole algorithm, the cost of an FMM matrix vector multiply is reduced to O(N4/3). A multilevel fast multipole algorithm (MLFMA) is implemented, whose complexity is further reduced to O(NlogN). The FMM also requires less memory, and hence, can solve a larger problem on a small computer.",

author = "Song, {J. M.} and Chew, {Weng Cho}",

year = "1995",

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note = "Proceedings of the 1995 IEEE Antennas and Propagation Society International Symposium. Part 4 (of 4) ; Conference date: 18-06-1995 Through 23-06-1995",

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T1 - Fast multipole method solution of three dimensional integral equation

AU - Song, J. M.

AU - Chew, Weng Cho

PY - 1995/1/1

Y1 - 1995/1/1

N2 - The fast multipole method (FMM) speeds up the matrix-vector multiply in the conjugate gradient method when it is used to solve the matrix equation iteratively. In this paper, FMM is applied to solve the electromagnetic scattering from 3D arbitrary shape conducting bodies. The electric field integral equation (EFIE), magnetic field integral equation (MFIF), and combined field integral equation (CFIE) are considered. FMM formula for CFIE has been derived, which reduces the complexity of a matrix-vector multiply from O(N2) to O(N1.5), where N is the number of unknowns. With a nonnested method, using the ray-propagation fast multipole algorithm, the cost of an FMM matrix vector multiply is reduced to O(N4/3). A multilevel fast multipole algorithm (MLFMA) is implemented, whose complexity is further reduced to O(NlogN). The FMM also requires less memory, and hence, can solve a larger problem on a small computer.

AB - The fast multipole method (FMM) speeds up the matrix-vector multiply in the conjugate gradient method when it is used to solve the matrix equation iteratively. In this paper, FMM is applied to solve the electromagnetic scattering from 3D arbitrary shape conducting bodies. The electric field integral equation (EFIE), magnetic field integral equation (MFIF), and combined field integral equation (CFIE) are considered. FMM formula for CFIE has been derived, which reduces the complexity of a matrix-vector multiply from O(N2) to O(N1.5), where N is the number of unknowns. With a nonnested method, using the ray-propagation fast multipole algorithm, the cost of an FMM matrix vector multiply is reduced to O(N4/3). A multilevel fast multipole algorithm (MLFMA) is implemented, whose complexity is further reduced to O(NlogN). The FMM also requires less memory, and hence, can solve a larger problem on a small computer.

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M3 - Conference article

AN - SCOPUS:0029202007

VL - 3

SP - 1528

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JO - AP-S International Symposium (Digest) (IEEE Antennas and Propagation Society)

JF - AP-S International Symposium (Digest) (IEEE Antennas and Propagation Society)

SN - 0272-4693

T2 - Proceedings of the 1995 IEEE Antennas and Propagation Society International Symposium. Part 4 (of 4)

Y2 - 18 June 1995 through 23 June 1995

ER -

Fast multipole method solution of three dimensional integral equation

Abstract

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