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

The diagonally perturbed incomplete factorization preconditioning scheme is applied to the conjugate gradient (CG) method fur 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. Index Terms--Conjugate gradient (CG) method, finite-element method (FEM), incomplete factorization, preconditioning technique.