Parallel realization of algebraic domain decomposition for the vector finite element analysis of 3D time-harmonic EM field problems

Abstract

SUMMARYBased on message passing interface (MPI) distributed-memory network, we propose a parallel realization of algebraic domain decomposition method to solve the large sparse linear systems, which were derived from the vector finite element method (FEM) for three-dimensional electromagnetic field problems. The proposed method segments the problem into several smaller sub-problems, solves each sub-problem in each node (i.e. computer) by the direct method, exchanges related data between nodes with MPI cluster network, and then reassembles the sub-problem solutions together to get the global result. Multifrontal method is applied to solve intermediate equations associated with each sub-problem and conjugate gradient methods are used to solve the reduced interface system. The simulation results demonstrate that the proposed parallel computing can save much more memory and CPU time than sequential computing. Furthermore, it can solve larger system in reasonable time and get excellent performance vs price ratio.

Application of algebraic domain decomposition combined with Krylov subspace iterative methods to solve 3D vector finite element equations

“…Of the Krylov iterative methods, the conjugate gradient (CGN applied to normal equations), BCG, and GMRES methods are most popular and suitable for solving nondefinite systems. For comparison, we choose these three methods in our investigation to solve the reduced interface system and compare their efficiency when applied to our problems [18,19]. The intermediate equations associated with each subproblem can be solved with a suitable solver according to their characteristics.…”