SSMR Preconditioned Linear Iterative Solvers for Electromagnetic Simulations

This paper presents a new preconditioner based on a Successive Minimal Residual (SMR) method. The SMR method is based on the Successive Over-Relaxation (SOR) method. Convergence property of the SOR method depends on a relaxation parameter, but its optimal value can be hardly computed. The authors resolve the aforementioned problem under a minimal condition for an intermediate residual in the successive computation of the SOR method. Features of the SMR method are that the convergence rate is poor but the computational and memory costs are light compared with the Krylov subspace methods. Then the authors use the SMR method for preconditioning technique. A numerical experiment treats a small scale practical electromagnetic problem followed by a complex symmetric linear system of equations. The SMR preconditioning insensibly refines the convergence rate of the Conjugate Orthgonal Conjugate Gradient (COCG) method suitable for symmetric coefficient matrix.