Parallel Domain Decomposition Methods for High-Order Finite Element Solutions of the Helmholtz Problem

摘要

The article is concerned with a parallel iterative domain decomposition algorithm for high-order finite element solutions of the Helmholtz wave equation. The iteration is performed in a block-Jacobi manner. For the interface operator, a Robin interface boundary condition is employed in a modified form which allows possible discontinuities of the discrete normal flux on the subdomain interfaces. The convergence of the algorithm is analyzed using energy estimates. Numerical results are given to show the effectiveness and parallel efficiency of the algorithm for the simulation of high-frequency waves in heterogeneous media in the two-dimensional space. The algorithm is carried out on a 16-node Linux cluster; it has been observed more than 97% parallel efficiency for all tested problems.