A highly effective preconditioner for solving the finite element-boundary integral matrix equation of 3-D scattering

Jian Liu; Jian Ming Jin

doi:10.1109/TAP.2002.801377

A highly effective preconditioner for solving the finite element-boundary integral matrix equation of 3-D scattering

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Abstract

A highly effective preconditioner is presented for solving the system of equations obtained from the application of the hybrid finite element-boundary integral (FE-BI) method to three-dimensional (3-D) electromagnetic scattering problems. Different from widely used algebraic preconditioners, the proposed one is based on a physical approximation and is constructed from the finite element method (FEM) using an absorbing boundary condition (ABC) on the truncation boundary. It is shown that the large eigenvalues of the finite element (FE)-ABC system are similar to those of the FE-BI system. Hence, the preconditioned system has a spectrum distribution clustered around 1 in the complex plane. Consequently, when a Krylov subspace based method is employed to solve the preconditioned system, the convergence can be greatly accelerated. Numerical results show that the proposed preconditioner can improve the convergence of an iterative solution by approximately two orders of magnitude for large problems.

Original language	English (US)
Pages (from-to)	1212-1221
Number of pages	10
Journal	IEEE Transactions on Antennas and Propagation
Volume	50
Issue number	9
DOIs	https://doi.org/10.1109/TAP.2002.801377
State	Published - Sep 2002

Keywords

Absorbing boundary condition (ABC)
Boundary integral equation (BIE)
Electromagnetic scattering
Finite element method (FEM)
Numerical analysis
Preconditioner

ASJC Scopus subject areas

Electrical and Electronic Engineering

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10.1109/TAP.2002.801377

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title = "A highly effective preconditioner for solving the finite element-boundary integral matrix equation of 3-D scattering",

abstract = "A highly effective preconditioner is presented for solving the system of equations obtained from the application of the hybrid finite element-boundary integral (FE-BI) method to three-dimensional (3-D) electromagnetic scattering problems. Different from widely used algebraic preconditioners, the proposed one is based on a physical approximation and is constructed from the finite element method (FEM) using an absorbing boundary condition (ABC) on the truncation boundary. It is shown that the large eigenvalues of the finite element (FE)-ABC system are similar to those of the FE-BI system. Hence, the preconditioned system has a spectrum distribution clustered around 1 in the complex plane. Consequently, when a Krylov subspace based method is employed to solve the preconditioned system, the convergence can be greatly accelerated. Numerical results show that the proposed preconditioner can improve the convergence of an iterative solution by approximately two orders of magnitude for large problems.",

keywords = "Absorbing boundary condition (ABC), Boundary integral equation (BIE), Electromagnetic scattering, Finite element method (FEM), Numerical analysis, Preconditioner",

author = "Jian Liu and Jin, {Jian Ming}",

note = "Funding Information: Manuscript received April 21, 2001; revised August 7, 2001. This work was supported in part by a grant from AFOSR via the MURI Program under Contract F49620-96-1-0025, and in part by a grant from ONR under Contract N00014-01-1-0210.",

year = "2002",

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AU - Liu, Jian

AU - Jin, Jian Ming

N1 - Funding Information: Manuscript received April 21, 2001; revised August 7, 2001. This work was supported in part by a grant from AFOSR via the MURI Program under Contract F49620-96-1-0025, and in part by a grant from ONR under Contract N00014-01-1-0210.

PY - 2002/9

Y1 - 2002/9

N2 - A highly effective preconditioner is presented for solving the system of equations obtained from the application of the hybrid finite element-boundary integral (FE-BI) method to three-dimensional (3-D) electromagnetic scattering problems. Different from widely used algebraic preconditioners, the proposed one is based on a physical approximation and is constructed from the finite element method (FEM) using an absorbing boundary condition (ABC) on the truncation boundary. It is shown that the large eigenvalues of the finite element (FE)-ABC system are similar to those of the FE-BI system. Hence, the preconditioned system has a spectrum distribution clustered around 1 in the complex plane. Consequently, when a Krylov subspace based method is employed to solve the preconditioned system, the convergence can be greatly accelerated. Numerical results show that the proposed preconditioner can improve the convergence of an iterative solution by approximately two orders of magnitude for large problems.

AB - A highly effective preconditioner is presented for solving the system of equations obtained from the application of the hybrid finite element-boundary integral (FE-BI) method to three-dimensional (3-D) electromagnetic scattering problems. Different from widely used algebraic preconditioners, the proposed one is based on a physical approximation and is constructed from the finite element method (FEM) using an absorbing boundary condition (ABC) on the truncation boundary. It is shown that the large eigenvalues of the finite element (FE)-ABC system are similar to those of the FE-BI system. Hence, the preconditioned system has a spectrum distribution clustered around 1 in the complex plane. Consequently, when a Krylov subspace based method is employed to solve the preconditioned system, the convergence can be greatly accelerated. Numerical results show that the proposed preconditioner can improve the convergence of an iterative solution by approximately two orders of magnitude for large problems.

KW - Absorbing boundary condition (ABC)

KW - Boundary integral equation (BIE)

KW - Electromagnetic scattering

KW - Finite element method (FEM)

KW - Numerical analysis

KW - Preconditioner

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A highly effective preconditioner for solving the finite element-boundary integral matrix equation of 3-D scattering

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