The Use of Huygens’ Equivalence Principle for Solving 3-D Volume Integral Equation of Scattering

C. C. Chenga Lu; Weng Cho Chew

doi:10.1109/8.384194

The Use of Huygens’ Equivalence Principle for Solving 3-D Volume Integral Equation of Scattering

C. C. Chenga Lu, Weng Cho Chew

Electrical and Computer Engineering

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

38 Scopus citations

Abstract

A three-dimensional (3-D) version of the nested equivalent principle algorithm (NEPAL) is presented. In 3-D, a scatterer is first decomposed into N subscatterers. Then, spherical wave functions are used to represent the scattered field of the subscatterers. Subscatterers are divided into different levels of groups in a nested manner. For example, each group consists of eight subgroups, and each subgroup contains eight sub-subgroups, and so on. For each subgroup, the scattering solution is first solved and the number of subscatterers of the subgroup is then reduced by replacing the interior subscatterers with boundary subscatterers using Huygens’ equivalence principle. As a result, when the subgroups are combined to form a higher level group, the group will have a smaller number of subscatterers. This process is repeated for each level, and in the last level, the number of subscatterers is proportional to that of boundary size of the scatterers. This algorithm has a computational complexity of O(N2) in three dimensions for all excitations and has the advantage of solving large scattering problems for multiple excitations. This is in contrast to Gaussian elimination which has a computational complexity of O(V3).

Original language	English
Pages (from-to)	500-507
Number of pages	8
Journal	IEEE Transactions on Antennas and Propagation
Volume	43
Issue number	5
DOIs	https://doi.org/10.1109/8.384194
State	Published - May 1995

Bibliographical note

Funding Information:
Manuscript received July 7, 1994; revised November 30, 1994. This work was supported in part by Office of Naval Research Grant N00014-89-51286, the Army Research Office Contract DAAL03-91-G-0339, The National Science Foundation Grant NSF ECS 92-24466, NASA Grant NASA NAG 2-871, and the National Center for Supercomputing Applications (NCSA) at the University of Illinois, Urbana-Champaign. The authors are with the Department of Electrical and Computer Engineering, University of Illinois, Urbana, IL 61801 USA. IEEE Log Number 9410725.

Funding

Manuscript received July 7, 1994; revised November 30, 1994. This work was supported in part by Office of Naval Research Grant N00014-89-51286, the Army Research Office Contract DAAL03-91-G-0339, The National Science Foundation Grant NSF ECS 92-24466, NASA Grant NASA NAG 2-871, and the National Center for Supercomputing Applications (NCSA) at the University of Illinois, Urbana-Champaign. The authors are with the Department of Electrical and Computer Engineering, University of Illinois, Urbana, IL 61801 USA. IEEE Log Number 9410725.

Funders	Funder number
National Science Foundation (NSF)	NSF ECS 92-24466, NASA NAG 2-871
Office of Naval Research	N00014-89-51286
Army Research Office	DAAL03-91-G-0339
Beckman Institute for Advanced Science and Technology, University of Illinois, Urbana-Champaign

ASJC Scopus subject areas

Electrical and Electronic Engineering

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10.1109/8.384194

Cite this

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title = "The Use of Huygens{\textquoteright} Equivalence Principle for Solving 3-D Volume Integral Equation of Scattering",

abstract = "A three-dimensional (3-D) version of the nested equivalent principle algorithm (NEPAL) is presented. In 3-D, a scatterer is first decomposed into N subscatterers. Then, spherical wave functions are used to represent the scattered field of the subscatterers. Subscatterers are divided into different levels of groups in a nested manner. For example, each group consists of eight subgroups, and each subgroup contains eight sub-subgroups, and so on. For each subgroup, the scattering solution is first solved and the number of subscatterers of the subgroup is then reduced by replacing the interior subscatterers with boundary subscatterers using Huygens{\textquoteright} equivalence principle. As a result, when the subgroups are combined to form a higher level group, the group will have a smaller number of subscatterers. This process is repeated for each level, and in the last level, the number of subscatterers is proportional to that of boundary size of the scatterers. This algorithm has a computational complexity of O(N2) in three dimensions for all excitations and has the advantage of solving large scattering problems for multiple excitations. This is in contrast to Gaussian elimination which has a computational complexity of O(V3).",

author = "{Chenga Lu}, {C. C.} and Chew, {Weng Cho}",

note = "Funding Information: Manuscript received July 7, 1994; revised November 30, 1994. This work was supported in part by Office of Naval Research Grant N00014-89-51286, the Army Research Office Contract DAAL03-91-G-0339, The National Science Foundation Grant NSF ECS 92-24466, NASA Grant NASA NAG 2-871, and the National Center for Supercomputing Applications (NCSA) at the University of Illinois, Urbana-Champaign. The authors are with the Department of Electrical and Computer Engineering, University of Illinois, Urbana, IL 61801 USA. IEEE Log Number 9410725.",

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AU - Chenga Lu, C. C.

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N2 - A three-dimensional (3-D) version of the nested equivalent principle algorithm (NEPAL) is presented. In 3-D, a scatterer is first decomposed into N subscatterers. Then, spherical wave functions are used to represent the scattered field of the subscatterers. Subscatterers are divided into different levels of groups in a nested manner. For example, each group consists of eight subgroups, and each subgroup contains eight sub-subgroups, and so on. For each subgroup, the scattering solution is first solved and the number of subscatterers of the subgroup is then reduced by replacing the interior subscatterers with boundary subscatterers using Huygens’ equivalence principle. As a result, when the subgroups are combined to form a higher level group, the group will have a smaller number of subscatterers. This process is repeated for each level, and in the last level, the number of subscatterers is proportional to that of boundary size of the scatterers. This algorithm has a computational complexity of O(N2) in three dimensions for all excitations and has the advantage of solving large scattering problems for multiple excitations. This is in contrast to Gaussian elimination which has a computational complexity of O(V3).

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The Use of Huygens’ Equivalence Principle for Solving 3-D Volume Integral Equation of Scattering

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