Application of diagonally perturbed incomplete factorization preconditioned conjugate gradient algorithms for edge finite-element analysis of Helmholtz equations

Author

Chen, R.S. ; Ping, X.W. ; Yung, Edward K N ; Chan, C.H. ; Nie, Zaiping ; Hu, Jun

Author_Institution

Dept. of Commun. Eng., Nanjing Univ. of Sci. & Technol.

Volume

54

Issue

5

fYear

2006

fDate

5/1/2006 12:00:00 AM

Firstpage

1604

Lastpage

1608

Abstract

The diagonally perturbed incomplete factorization preconditioning scheme is applied to the conjugate gradient (CG) method for solving a large system of linear equations resulting from the use of edge-based finite-element method (FEM). This scheme contains more global information about the coefficient matrix when compared with banded-matrix schemes. The efficient implementation of this preconditioned CG (PCG) algorithm is described in detail for complex coefficient matrix equation. On several electromagnetic problems the PCG approach converges in CPU time, which is 8.6-19.5 times shorter with respect to the CG approach. By comparison with other preconditioned techniques, the results demonstrate that incomplete factorization preconditioning strategy is especially effective for CG iterative method when edge-FEM is applied to solve large-scale time-harmonic electromagnetic field problems

Keywords

Helmholtz equations; conjugate gradient methods; electromagnetic wave propagation; finite element analysis; matrix algebra; Helmholtz equation; complex coefficient matrix equation; conjugate gradient method; diagonally perturbed incomplete factorization; edge-based FEM; finite-element method; global information; preconditioned CG algorithm; time-harmonic electromagnetic field problem; Algorithm design and analysis; Character generation; Composite materials; Electric breakdown; Electromagnetic analysis; Electromagnetic fields; Equations; Finite element methods; Iterative methods; Large-scale systems; Conjugate gradient (CG) method; finite-element method (FEM); incomplete factorization; preconditioning technique;

fLanguage

English

Journal_Title

Antennas and Propagation, IEEE Transactions on

Publisher

ieee

ISSN

0018-926X

Type

jour

DOI

10.1109/TAP.2006.874358

Filename

1629293