TY - JOUR
T1 - Iterative Pure Source Transfer Domain Decomposition Methods for Helmholtz Equations in Heterogeneous Media
AU - Du , Yu
AU - Wu , Haijun
JO - Communications in Computational Physics
VL - 5
SP - 1247
EP - 1276
PY - 2023
DA - 2023/12
SN - 34
DO - http://doi.org/10.4208/cicp.OA-2023-0032
UR - https://global-sci.org/intro/article_detail/cicp/22213.html
KW - Helmholtz equation, large wave number, perfectly matched layer, source transfer, domain decomposition method, preconditioner, heterogeneous problem.
AB - <p style="text-align: justify;">We extend the pure source transfer domain decomposition method (PSTDDM) to solve the perfectly matched layer approximation of Helmholtz scattering
problems in heterogeneous media. We first propose some new source transfer operators, and then introduce the layer-wise and block-wise PSTDDMs based on these
operators. 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 problem
in the computational domain. Second, we propose the iterative layer-wise and block-wise PSTDDMs, which are designed by simply iterating the PSTDDM alternatively
over two staggered decompositions of the computational domain. Finally, extensive
numerical tests in two and three dimensions show that, as the preconditioner for the
GMRES method, the iterative PSTDDMs are more robust and efficient than PSTDDMs
for solving heterogeneous Helmholtz problems.</p>