2015/05/22 by Yu Du, Du, Yu, Haijun Wu +1
Engineering · Physics and Astronomy · #65N12 #65N15 #65N30 #78A40 #Electromagnetic Scattering and Analysis #Electromagnetic Simulation and Numerical Methods #FOS: Mathematics #G.1.0 #G.1.8 #Numerical Analysis (math.NA) #Numerical methods in engineering
paper · pdf · doi:10.48550/arxiv.1505.06052
openalex publication_date 2015/05/22 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
We propose a pure source transfer domain decomposition method (PSTDDM) for solving the truncated perfectly matched layer (PML) approximation in bounded domain of Helmholtz scattering problem. The method is a modification of the STDDM proposed by [Z. Chen and X. Xiang, SIAM J. Numer. Anal., 51 (2013), pp. 2331--2356]. After decomposing the domain into N non-overlapping layers, the STDDM is composed of two series steps of sources transfers and wave expansions, where N-1 truncated PML problems on two adjacent layers and N-2 truncated half-space PML problems are solved successively. While the PSTDDM consists merely of two parallel source transfer steps in two opposite directions, and in each step N-1 truncated PML problems on two adjacent layers are solved successively. One benefit of such a modification is that the truncated PML problems on two adjacent layers can be further solved by the PSTDDM along directions parallel to the layers. And therefore, we obtain a block-wise PSTDDM on the decomposition composed of N2 squares, which reduces the size of subdomain problems and is more suitable for large-scale problems. Convergences of both the layer-wise PSTDDM and the block-wise PSTDDM are proved for the case of constant wave number. Numerical examples are included to show that the PSTDDM gives good approximations to the discrete Helmholtz equations with constant wave numbers and can be used as an efficient preconditioner in the preconditioned GMRES method for solving the discrete Helmholtz equations with constant and heterogeneous wave numbers.