Application of a two-step preconditioning strategy to the finite element analysis for electromagnetic problems

A two-step preconditioning strategy is presented for the conjugate gradient (CG) iterative method to solve a large system of linear equations resulting from the use of edge-based finite-element discretizations of Helmholtz equations. The key idea is to combine both the factorized sparse approximate inverse (FSAI) and the symmetric successive overrelaxation (SSOR) preconditioning techniques in two successive steps in order to obtain a better preconditioner for the original matrix equations. The newly constructed preconditioner combines the advantages of both the FSAI and SSOR preconditioned with less computational complexity without the breakdowns of incomplete factorization technique. Numerical simulations show that this jointly preconditioned CG iterative method has a faster convergence speed than both FSAI and SSOR preconditioned CG methods. © 2006 Wiley Periodicals, Inc.