A parallel finite element algorithm for nonstationary incompressible magnetohydrodynamics equations

Abstract

Purpose The purpose of this paper is to design a parallel finite element (FE) algorithm based on fully overlapping domain decomposition for solving the nonstationary incompressible magnetohydrodynamics (MHD). Design/methodology/approach The fully discrete Euler implicit/explicit FE subproblems, which are defined in the whole domain with vast majority of the degrees of freedom associated with the particular subdomain, are solved in parallel. In each subproblem, the linear term is treated by implicit scheme and the nonlinear term is solved by explicit one. Findings For the algorithm, the almost unconditional convergence with optimal orders is validated by numerical tests. Some interesting phenomena are presented. Originality/value The proposed algorithm is effective, easy to realize with low communication costs and preferred for solving the strong nonlinear MHD system.