Special Session 43: Recent Advances in Inverse Problems, Imaging, and Their Applications

STDDM for the Helmholtz equation in inhomogeneous medium
Weiying Zheng
Academy of Mathematics and Systems Science, Chinese Academy of Sciences
Peoples Rep of China
Co-Author(s):    Yuhao Wang
Abstract:
In this talk, I will study the source-transfer-domain-decomposition method (STDDM) for solving high-frequency scattering problem of Helmholtz equation in a background medium with compact inhomogeneity. We first truncate the unbounded domain with the uniaxial perfectly matched layer (UPML) method. An wavenumber-explicit infsup condition is proved for the bilinear form of the truncated PML problem, where the infsup constant is shown to be $O(k\ln k)$, with $k$ being the wavenumber. Based on this infsup condition, we obtain preasymptotic finite element error estimates for the finite element approximation to the truncated problem. We propose an STDDM for solving the truncated PML problem and have proved the convergence of the method.