Iterative Pure Source Transfer Domain Decomposition Methods for Helmholtz Equations in Heterogeneous Media (Communications in Computational Physics, 2023)
We extend the pure source transfer domain decomposition method (PSTDDM) to solve the perfectly matched layer approximation of Helmholtz scatteringproblems in heterogeneous media. We first propose some new source transfer operators, and then introduce the layer-wise and block-wise PSTDDMs based on theseoperators. In particular, it is proved that the solution obtained by the layer-wise PSTDDM in $\mathbb{R}^2$ coincides with the exact solution to the heterogeneous Helmholtz problemin the computational domain. Second, we propose the iterative layer-wise and block-wise PSTDDMs, which are designed by simply iterating the PSTDDM alternativelyover two staggered decompositions of the computational domain. Finally, extensivenumerical tests in two and three dimensions show that, as the preconditioner for theGMRES method, the iterative PSTDDMs are more robust and efficient than PSTDDMsfor solving heterogeneous Helmholtz problems.