Double Source Transfer Domain Decomposition Method For Helmholtz Problems (Communications in Computational Physics, 2019)
We propose and study a double source transfer domain decomposition method (Double STDDM) for solving the truncated perfectly matched layer approximation in the bounded domain of Helmholtz problems. Based on the decomposition ofthe domain into non-overlapping layers and instead of transferring the source alongone direction in STDDM [Z. Chen and X. Xiang, 2013], Double STDDM transfers thesource in each layer along two directions, which can capture of the reflection information for heterogenous media. Double STDDM is an iterative scheme, and in eachiteration, it first transfers the source from down to up and produces the Up wave (thewave propagating from down to up), and then transfers the source from up to downand produces the Down wave (the wave propagating from up to down). The outputof Double STDDM is the summation of the Up and Down waves that are producedduring the iteration. By using the fundamental solution of the PML equation, the convergence of Double STDDM is proved for the case of a constant wavenumber.Numerical examples are included to show the efficient performance of using DoubleSTDDM as a preconditioner both for the problems with constant and heterogenouswavenumbers. For problems with a low velocity contrast, the number of iterationsis independent of the wavenumber and mesh size, whereas for problems with a highvelocity contrast, double STDDM performs much better than STDDM.