论文信息 - Effect of Preconditioning in Edge-Based Finite-Element Method

Effect of Preconditioning in Edge-Based Finite-Element Method

This paper discusses mathematical properties of preconditioned finite-element matrices based on vector potential formulation (A method) and vector and scalar potential formulation (A-V method) for eddy-current problems. Numerical results show that A-V method with preconditioning is stable at all frequencies in contrast to A method. In this paper, this property is mathematically discussed by considering the diagonal scaling which is one of the simple preconditioning methods. In addition, regularization of A method is discussed.

H. Igarashi | H. Igarashi | N. Yamamoto | N. Yamamoto

[1] H. Igarashi,et al. On convergence of ICCG applied to finite-element equation for quasi-static fields , 2002 .

[2] Per Christian Hansen,et al. Rank-Deficient and Discrete Ill-Posed Problems , 1996 .

[3] A. Bossavit. "Stiff" problems in eddy-current theory and the regularization of Maxwell's equations , 2001 .

[4] Hajime Igarashi,et al. Convergence of preconditioned conjugate gradient method applied to driven microwave problems , 2003 .

[5] Gene H. Golub,et al. Matrix computations (3rd ed.) , 1996 .

[6] Hajime Igarashi,et al. On the property of the curl-curl matrix in finite element analysis with edge elements , 2001 .