Solving EM scattering from complicated multi-scale objects by integral equation-domain decomposition method with recycling Krylov subspace method

Integral equation domain decomposition method (IE-DDM) is a very effective method for multi-scale time-harmonic electromagnetic problem. IE-DDM can improve the ill-conditioned matrix of the multi-scale problem, yield rapid convergence in the Krylov iterative solution process. In this paper, we use the Inner-Outer Krylov iteration technique to solve the matrix more stably by employing the DDM as an effective pre-conditioner. To speed up the computations of the sub-domains, a recycling Krylov subspace method GCRO with deflated restarting (GCRO-DR) is used. at the same time, the sparse approximation inverse (SAI) precondition technique is also applied to achieve fast convergence. Several complicated multi-scale cases are investigated to demonstrate the validity and ability of the present method.