A state-of-the-art linear solver IDR(s) method for large scale electromagnetic multiple scattering simulations

Abstract

This paper remarks IDR(s) method as an alternative solver for GMRES(m) method. A preconditioned IDR(s) algorithm is presented. Performance evaluations are done for the computation of the dense linear system of equations of order 105 followed by BEM analysis of EM multiple scattering. IDR(s) method with the optimal parameters (5 ≤ s ≤ 10) converges faster than GMRES(m max ) method, using small amount of memory rather than GMRES(50) method. Moreover, as the problem scale becomes larger, the bigger difference of convergence between IDR(s) method and GMRES(m max ) happens. We conclude therefore that IDR(s) method is better than the GMRES method with large restart cycles in terms of not only memory efficiency but also convergence We use the additional operations, but the accuracy fails for large s. The modifications of them may be an important subject.