TY - JOUR
T1 - Double Source Transfer Domain Decomposition Method For Helmholtz Problems
AU - Xueshuang Xiang
JO - Communications in Computational Physics
VL - 2
SP - 434
EP - 468
PY - 2019
DA - 2019/04
SN - 26
DO - http://doi.org/10.4208/cicp.OA-2018-0063
UR - https://global-sci.org/intro/article_detail/cicp/13098.html
KW - Helmholtz equation, high frequency waves, perfect matched layers, source transfer
domain decomposition method.
AB - <p style="text-align: justify;">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 of
the domain into non-overlapping layers and instead of transferring the source along
one direction in STDDM [Z. Chen and X. Xiang, 2013], Double STDDM transfers the
source in each layer along two directions, which can capture of the reflection information for heterogenous media. Double STDDM is an iterative scheme, and in each
iteration, it first transfers the source from down to up and produces the Up wave (the
wave propagating from down to up), and then transfers the source from up to down
and produces the Down wave (the wave propagating from up to down). The output
of Double STDDM is the summation of the Up and Down waves that are produced
during 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.<br/>Numerical examples are included to show the efficient performance of using Double
STDDM as a preconditioner both for the problems with constant and heterogenous
wavenumbers. For problems with a low velocity contrast, the number of iterations
is independent of the wavenumber and mesh size, whereas for problems with a high
velocity contrast, double STDDM performs much better than STDDM.</p>