On the formulation of hybrid finite-element and boundary-integral methods for 3-D scattering

Xin Qing Sheng; Jian Ming Jin; Cai Cheng Lu; Weng Cho Chew

doi:10.1109/8.662648

On the formulation of hybrid finite-element and boundary-integral methods for 3-D scattering

Xin Qing Sheng, Jian Ming Jin, Cai Cheng Lu, Weng Cho Chew

Electrical and Computer Engineering

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

270 Scopus citations

Abstract

This paper studies, in detail, a variety of formulations for the hybrid finite-element and boundary-integral (FE-BI) method for three-dimensional (3-D) electromagnetic scattering by inhomogeneous objects. It is shown that the efficiency and accuracy of the FE-BI method depends highly on the formulation and discretization of the boundary-integral equation (BIE) used. A simple analysis of the matrix condition number identifies the efficiency of the different FE-BI formulations and an analysis of weighting functions shows that the traditional FE-BI formulations cannot produce accurate solutions. A new formulation is then proposed and numerical results show that the resulting solution has a good efficiency and accuracy and is completely immune to the problem of interior resonance. Finally, the multilevel fast multipole algorithm (MLFMA) is employed to significantly reduce the memory requirement and computational complexity of the proposed FE-BI method.

Original language	English
Pages (from-to)	303-311
Number of pages	9
Journal	IEEE Transactions on Antennas and Propagation
Volume	46
Issue number	3
DOIs	https://doi.org/10.1109/8.662648
State	Published - 1998

Bibliographical note

Funding Information:
Manuscript received May 6, 1997; revised October 20, 1997. This work was supported by the Office of Naval Research under Grant N00014-95-1-0848, by a Grant from the Air Force Office of Scientific Research via the MURI Program under Contract F49620-96-1-0025, and by the National Science Foundation under Grant NSF ECE 94-57735.

Funding

Manuscript received May 6, 1997; revised October 20, 1997. This work was supported by the Office of Naval Research under Grant N00014-95-1-0848, by a Grant from the Air Force Office of Scientific Research via the MURI Program under Contract F49620-96-1-0025, and by the National Science Foundation under Grant NSF ECE 94-57735.

Funders	Funder number
National Science Foundation Arctic Social Science Program	NSF ECE 94-57735
Office of Naval Research Naval Academy	N00014-95-1-0848
Air Force Office of Scientific Research, United States Air Force
Multidisciplinary University Research Initiative	F49620-96-1-0025

Keywords

Boundary-integral equations
Electromagnetic scattering
Finite-element methods
Nonhomogeneous media

ASJC Scopus subject areas

Electrical and Electronic Engineering

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10.1109/8.662648

Cite this

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title = "On the formulation of hybrid finite-element and boundary-integral methods for 3-D scattering",

abstract = "This paper studies, in detail, a variety of formulations for the hybrid finite-element and boundary-integral (FE-BI) method for three-dimensional (3-D) electromagnetic scattering by inhomogeneous objects. It is shown that the efficiency and accuracy of the FE-BI method depends highly on the formulation and discretization of the boundary-integral equation (BIE) used. A simple analysis of the matrix condition number identifies the efficiency of the different FE-BI formulations and an analysis of weighting functions shows that the traditional FE-BI formulations cannot produce accurate solutions. A new formulation is then proposed and numerical results show that the resulting solution has a good efficiency and accuracy and is completely immune to the problem of interior resonance. Finally, the multilevel fast multipole algorithm (MLFMA) is employed to significantly reduce the memory requirement and computational complexity of the proposed FE-BI method.",

keywords = "Boundary-integral equations, Electromagnetic scattering, Finite-element methods, Nonhomogeneous media",

author = "Sheng, {Xin Qing} and Jin, {Jian Ming} and Lu, {Cai Cheng} and Chew, {Weng Cho}",

note = "Funding Information: Manuscript received May 6, 1997; revised October 20, 1997. This work was supported by the Office of Naval Research under Grant N00014-95-1-0848, by a Grant from the Air Force Office of Scientific Research via the MURI Program under Contract F49620-96-1-0025, and by the National Science Foundation under Grant NSF ECE 94-57735.",

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T1 - On the formulation of hybrid finite-element and boundary-integral methods for 3-D scattering

AU - Sheng, Xin Qing

AU - Jin, Jian Ming

AU - Lu, Cai Cheng

AU - Chew, Weng Cho

N1 - Funding Information: Manuscript received May 6, 1997; revised October 20, 1997. This work was supported by the Office of Naval Research under Grant N00014-95-1-0848, by a Grant from the Air Force Office of Scientific Research via the MURI Program under Contract F49620-96-1-0025, and by the National Science Foundation under Grant NSF ECE 94-57735.

PY - 1998

Y1 - 1998

N2 - This paper studies, in detail, a variety of formulations for the hybrid finite-element and boundary-integral (FE-BI) method for three-dimensional (3-D) electromagnetic scattering by inhomogeneous objects. It is shown that the efficiency and accuracy of the FE-BI method depends highly on the formulation and discretization of the boundary-integral equation (BIE) used. A simple analysis of the matrix condition number identifies the efficiency of the different FE-BI formulations and an analysis of weighting functions shows that the traditional FE-BI formulations cannot produce accurate solutions. A new formulation is then proposed and numerical results show that the resulting solution has a good efficiency and accuracy and is completely immune to the problem of interior resonance. Finally, the multilevel fast multipole algorithm (MLFMA) is employed to significantly reduce the memory requirement and computational complexity of the proposed FE-BI method.

AB - This paper studies, in detail, a variety of formulations for the hybrid finite-element and boundary-integral (FE-BI) method for three-dimensional (3-D) electromagnetic scattering by inhomogeneous objects. It is shown that the efficiency and accuracy of the FE-BI method depends highly on the formulation and discretization of the boundary-integral equation (BIE) used. A simple analysis of the matrix condition number identifies the efficiency of the different FE-BI formulations and an analysis of weighting functions shows that the traditional FE-BI formulations cannot produce accurate solutions. A new formulation is then proposed and numerical results show that the resulting solution has a good efficiency and accuracy and is completely immune to the problem of interior resonance. Finally, the multilevel fast multipole algorithm (MLFMA) is employed to significantly reduce the memory requirement and computational complexity of the proposed FE-BI method.

KW - Boundary-integral equations

KW - Electromagnetic scattering

KW - Finite-element methods

KW - Nonhomogeneous media

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On the formulation of hybrid finite-element and boundary-integral methods for 3-D scattering

Abstract

Bibliographical note

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Keywords

ASJC Scopus subject areas

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