A multilevel algorithm for solving a boundary integral equation of wave scattering

Cai‐Cheng ‐C Lu; Weng Cho Chew

doi:10.1002/mop.4650071013

A multilevel algorithm for solving a boundary integral equation of wave scattering

Cai‐Cheng ‐C Lu, Weng Cho Chew

Electrical and Computer Engineering

Research output: Contribution to journal › Article › peer-review

301 Scopus citations

Abstract

In the solution of an integral equation using the conjugate gradient (CG) method, the most expensive part is the matrix‐vector multiplication, requiring O(N²) floating‐point operations. The fast multipole method (FMM) reduced the operation to O(N¹⁵). In this article we apply a multilevel algorithm to this problem and show that the complexity of a matrix‐vector multiplication is proportional to N (log(N))². © 1994 John Wiley & Sons, Inc.

Original language	English
Pages (from-to)	466-470
Number of pages	5
Journal	Microwave and Optical Technology Letters
Volume	7
Issue number	10
DOIs	https://doi.org/10.1002/mop.4650071013
State	Published - Jul 1994

Keywords

Fast multipole algorithm
boundary integral equation
multilevel algorithm
numerical methods
wave scattering

ASJC Scopus subject areas

Electronic, Optical and Magnetic Materials
Atomic and Molecular Physics, and Optics
Condensed Matter Physics
Electrical and Electronic Engineering

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10.1002/mop.4650071013

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abstract = "In the solution of an integral equation using the conjugate gradient (CG) method, the most expensive part is the matrix‐vector multiplication, requiring O(N2) floating‐point operations. The fast multipole method (FMM) reduced the operation to O(N15). In this article we apply a multilevel algorithm to this problem and show that the complexity of a matrix‐vector multiplication is proportional to N (log(N))2. {\textcopyright} 1994 John Wiley & Sons, Inc.",

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AU - Chew, Weng Cho

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N2 - In the solution of an integral equation using the conjugate gradient (CG) method, the most expensive part is the matrix‐vector multiplication, requiring O(N2) floating‐point operations. The fast multipole method (FMM) reduced the operation to O(N15). In this article we apply a multilevel algorithm to this problem and show that the complexity of a matrix‐vector multiplication is proportional to N (log(N))2. © 1994 John Wiley & Sons, Inc.

AB - In the solution of an integral equation using the conjugate gradient (CG) method, the most expensive part is the matrix‐vector multiplication, requiring O(N2) floating‐point operations. The fast multipole method (FMM) reduced the operation to O(N15). In this article we apply a multilevel algorithm to this problem and show that the complexity of a matrix‐vector multiplication is proportional to N (log(N))2. © 1994 John Wiley & Sons, Inc.

KW - Fast multipole algorithm

KW - boundary integral equation

KW - multilevel algorithm

KW - numerical methods

KW - wave scattering

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JO - Microwave and Optical Technology Letters

JF - Microwave and Optical Technology Letters

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ER -

A multilevel algorithm for solving a boundary integral equation of wave scattering

Abstract

Keywords

ASJC Scopus subject areas

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