Application of robust incomplete Cholesky factorizations preconditioned CG algorithms for FEM analysis of millimeter wave filters

The Incomplete Cholesky factorizations preconditioning scheme is applied to the conjugate gradient (CG) method for solving a large system of linear equations resulting from finite element method (FEM) analysis of millimeter wave filters. As is well known, the convergence of CG method deteriorates with increasing EM wave number and in millimeter wave band the eigen-values of A are more and more scattered between both the right and the left half-plane. The efficient implementation of this preconditioned CG (PCG) algorithm is described in details for complex coefficient matrix. With incomplete factorization preconditioning scheme in the conjugate gradient algorithm, this PCG approach can reach convergence in 20 times CPU time shorter than CG for several typical millimeter wave structures.