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Progress In Electromagnetics Research
ISSN: 1070-4698, E-ISSN: 1559-8985
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AN EFFICIENT APPROACH FOR MULTIFRONTAL ALGORITHM TO SOLVE NON-POSITIVE-DEFINITE FINITE ELEMENT EQUATIONS IN ELECTROMAGNETIC PROBLEMS

By J. Tian, Z.-Q. Lv, X.-W. Shi, L. Xu, and F. Wei

Full Article PDF (2,122 KB)

Abstract:
A new method called Expanded Cholesky Method (ECM) is proposed in this paper. The method can be used to decompose sparse symmetric non-positive-definite finite element (FEM) matrices. There are some advantages of the ECM, such as low storage, simplicity and easy parallelization. Based on the method, multifrontal (MF) algorithm is applied in non-positive-definite FEM computation. Numerical results show that the hybrid ECM/MF algorithm is stable and effective. In comparison with Generalized Minimal Residual Method (GMRES) in FEM electromagnetic computation, hybrid ECM/MF technology has distinct advantages in precision. The proposed method can be used to calculate a class of non-positive-definite electromagnetic problems.

Citation:
J. Tian, Z.-Q. Lv, X.-W. Shi, L. Xu, and F. Wei, "An Efficient Approach for Multifrontal Algorithm to Solve Non-Positive-Definite Finite Element Equations in Electromagnetic Problems," Progress In Electromagnetics Research, Vol. 95, 121-133, 2009.
doi:10.2528/PIER09070207
http://www.jpier.org/PIER/pier.php?paper=09070207

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