Relaxed Incomplete Cholesky Factorization Preconditioned Symmetric LBCG Algorithm for Solving Electromagnetic Problems

Abstract

The symmetric linear biconjugate gradient (S-LBCG) iterative algorithm combined with modified relaxed incomplete Cholesky (RIC) preconditioner is proposed for solving large sparse complex symmetric and highly indefinite systems, which results from the use of edge-based finite-element method (FEM) on the analysis of electromagnetic problems. The S-LBCG iterative algorithm is derived from the linear biconjugate gradient iterative algorithm. It contains only one matrix-vector product per iteration for solving complex sparse symmetric systems. The preconditioner is derived from the relaxed incomplete Cholesky factorization with diagonal compensation. More robust and efficient RIC preconditioner can be achieved by employing preprocessing scheme of scaling and reordering before the incomplete factorization. Numerical tests on analysis of time-harmonic electromagnetic field problems show that this RIC preconditioned S-LBCG algorithm performs excellently both on reducing the memory requirement and on convergence rate.