The Use of Huygens' Equivalence Principle for Solving the Volume Integral Equation of Scattering

Weng Cho Chew; Cai Cheng Lu

doi:10.1109/8.237620

The Use of Huygens' Equivalence Principle for Solving the Volume Integral Equation of Scattering

Weng Cho Chew, Cai Cheng Lu

Electrical and Computer Engineering

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

70 Scopus citations

Abstract

A new algorithm is introduced to solve the volume integral equation of scattering. A volume scatterer is first divided into N subscatterers. Then the subscatterers are divided into four groups, and the groups are in turn divided into four subgroups and so on. By using the idea found in many fast algorithms, a smaller problem can hence be nested within a larger problem. Moreover, by way of Huygens' equivalence principle, the scattering properties of a group of subscatterers in a volume can be replaced by a group of subscatterers distributed on a surface enclosing the volume. Based on this idea, we present an algorithm which solves the scattering problem by several stages, where at each stage the interaction matrix algorithm is first used to find the scattering solution of each subgroup of subscatterers. Subscatterers are then replaced by equivalent surface subscatterers which are used in the next stage. Consequently, this results in a reduction in the number of subscatterers at every stage. This algorithm can be shown to have a CPU time asymptotically proportional to N1.5 for N subscatterers.

Original language	English
Pages (from-to)	897-904
Number of pages	8
Journal	IEEE Transactions on Antennas and Propagation
Volume	41
Issue number	7
DOIs	https://doi.org/10.1109/8.237620
State	Published - Jul 1993

Bibliographical note

Funding Information:
Manuscript received March 26, 1992; revised February 12, 1993. This work was supported by the Office of Naval Research under grant N00014-89-51286 and by the Army Research Office under contract DAAL03-91-G-0339. The computer time was provided by the National Center for Supercomputing Applications (NCSA) at the University of Illinois, Urbana-Champaign.

Funding

Manuscript received March 26, 1992; revised February 12, 1993. This work was supported by the Office of Naval Research under grant N00014-89-51286 and by the Army Research Office under contract DAAL03-91-G-0339. The computer time was provided by the National Center for Supercomputing Applications (NCSA) at the University of Illinois, Urbana-Champaign.

Funders	Funder number
Office of Naval Research	N00014-89-51286
Army Research Office	DAAL03-91-G-0339

ASJC Scopus subject areas

Electrical and Electronic Engineering

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10.1109/8.237620

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title = "The Use of Huygens' Equivalence Principle for Solving the Volume Integral Equation of Scattering",

abstract = "A new algorithm is introduced to solve the volume integral equation of scattering. A volume scatterer is first divided into N subscatterers. Then the subscatterers are divided into four groups, and the groups are in turn divided into four subgroups and so on. By using the idea found in many fast algorithms, a smaller problem can hence be nested within a larger problem. Moreover, by way of Huygens' equivalence principle, the scattering properties of a group of subscatterers in a volume can be replaced by a group of subscatterers distributed on a surface enclosing the volume. Based on this idea, we present an algorithm which solves the scattering problem by several stages, where at each stage the interaction matrix algorithm is first used to find the scattering solution of each subgroup of subscatterers. Subscatterers are then replaced by equivalent surface subscatterers which are used in the next stage. Consequently, this results in a reduction in the number of subscatterers at every stage. This algorithm can be shown to have a CPU time asymptotically proportional to N1.5 for N subscatterers.",

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note = "Funding Information: Manuscript received March 26, 1992; revised February 12, 1993. This work was supported by the Office of Naval Research under grant N00014-89-51286 and by the Army Research Office under contract DAAL03-91-G-0339. The computer time was provided by the National Center for Supercomputing Applications (NCSA) at the University of Illinois, Urbana-Champaign.",

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N2 - A new algorithm is introduced to solve the volume integral equation of scattering. A volume scatterer is first divided into N subscatterers. Then the subscatterers are divided into four groups, and the groups are in turn divided into four subgroups and so on. By using the idea found in many fast algorithms, a smaller problem can hence be nested within a larger problem. Moreover, by way of Huygens' equivalence principle, the scattering properties of a group of subscatterers in a volume can be replaced by a group of subscatterers distributed on a surface enclosing the volume. Based on this idea, we present an algorithm which solves the scattering problem by several stages, where at each stage the interaction matrix algorithm is first used to find the scattering solution of each subgroup of subscatterers. Subscatterers are then replaced by equivalent surface subscatterers which are used in the next stage. Consequently, this results in a reduction in the number of subscatterers at every stage. This algorithm can be shown to have a CPU time asymptotically proportional to N1.5 for N subscatterers.

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The Use of Huygens' Equivalence Principle for Solving the Volume Integral Equation of Scattering

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