Parallel SDDM with communication-avoiding BICGSTAB for large-scale 3D scattering problems

In the parallel finite element domain decomposition methods (FEM-DDM), one of the key step is to solve the reduced linear system defined on the subdomain interfaces iteratively using a Krylov subspace method such as the biconjugate gradient stabilized (BICGSTAB) method. In each iteration of BICGSTAB, multiple global MPI communication collectives are required, which are becoming increasingly expensive when many processors are used on modern computers, especially on a large-scale system. To address this limitation, a communication-avoiding variant of BICGSTAB (CA-BICGSTAB) is realized and implemented to minimize global communication therefore improve massively parallel efficiency of the FEM-DDM in this paper. A series of numerical examples are presented to demonstrate the superior performance of CA-BICGSTAB over conventional BICGSTAB.