Application of the preconditioned conjugate-gradient algorithm to the edge FEM for electromagnetic boundary-value problems

In this letter, an effective symmetric successive overrelaxation (SSOR) preconditioning scheme is applied to the conjugate-gradient method for solving a large system of linear equations resulting from the use of the edge-based finite-element method (FEM). With SSOR as the preconditioner as well as its efficient implementation in the conjugate-gradient (CG) algorithm, the PCG method converges five times as fast as the CG method. This result demonstrates that SSOR is a good preconditioner for the CG iterative method when the FEM is applied to solve large-scale electromagnetic problems. © 2000 John Wiley & Sons, Inc. Microwave Opt Technol Lett 27: 235–238, 2000.

[1]  Jin-Fa Lee,et al.  A perfectly matched anisotropic absorber for use as an absorbing boundary condition , 1995 .

[2]  J. F. Scholl,et al.  Diagonal preconditioners for the EFIE using a wavelet basis , 1996 .

[3]  O. Axelsson,et al.  On the rate of convergence of the preconditioned conjugate gradient method , 1986 .

[4]  R. P. Kendall,et al.  An Approximate Factorization Procedure for Solving Self-Adjoint Elliptic Difference Equations , 1968 .

[5]  Tapan K. Sarkar,et al.  On a class of finite step iterative methods (Conjugate directions) for the solution of an operator equation arising in electromagnetics , 1985 .

[6]  Weng Cho Chew,et al.  Numerical Study of Approximate Inverse Preconditioner for Two-Dimensional Engine Inlet Problems , 1999 .

[7]  D. Kershaw The incomplete Cholesky—conjugate gradient method for the iterative solution of systems of linear equations , 1978 .

[8]  Jian-Ming Jin,et al.  The Finite Element Method in Electromagnetics , 1993 .

[9]  Masanori Koshiba,et al.  Three-dimensional finite-element method with edge elements for electromagnetic waveguide discontinuities , 1991 .

[10]  Akira Ishimaru,et al.  A Banded Matrix Iterative Approach to Monte Carlo Simulations Of Large-Scale Random Rough Surface Scattering: TE Case , 1993 .

[11]  Raj Mittra,et al.  A note on the application of edge-elements for modeling three-dimensional inhomogeneously-filled cavities , 1992 .

[12]  A. Yaghjian,et al.  Banded-matrix preconditioning for electric-field integral equations , 1997, IEEE Antennas and Propagation Society International Symposium 1997. Digest.

[13]  D. Novak,et al.  37-GHz fiber-wireless system for distribution of broad-band signals , 1997 .

[14]  Stephen J. Wright,et al.  Conjugate Gradient Methods , 1999 .