Parallel FEM-DDM with BD-SGS Preconditioner for 3D Scattering by Large Inhomogeneous Objects

We present in this paper a flexible and efficient block diagonal symmetric Gauss-Seidel (BD-SGS) preconditioner for the hierarchical parallel FEM-DDM. In the hierarchical domain decomposition scheme, the whole FEM solution domain is first decomposed into large size subdomains with a total number equals to MPI processes. Then, each large subdomain is distributed to a MPI process and further decomposed into smaller ones to achieve good computation efficiency. Our preconditioner is based on this hierarchical parallel structure. It is specially designed to accelerate the convergence of iterative solution and reduce both the time and memory consumption of the reduced interface problems from FEM-DDM by constructing symmetric Gauss-Seidel preconditioner (SGS) for each large subdomain. Numerical examples are presented to demonstrate the efficiency, scalability, and capability of this specially designed BD-SGS preconditioner.