A SOURCE TRANSFER DOMAIN DECOMPOSITION METHOD FOR HELMHOLTZ EQUATIONS IN UNBOUNDED DOMAIN

• Published in: SIAM journal on numerical analysis Vol. 51; no. 4; pp. 2331 - 2356
• Main Authors: CHEN, ZHIMING, XIANG, XUESHUANG
• Format: Journal Article
• Language: English
• Published: Philadelphia Society for Industrial and Applied Mathematics 01-01-2013
• Subjects: Acoustic scattering; Applied mathematics; Approximation; Computational mathematics; Constants; Convergence; Coordinate systems; Decomposition; Decomposition methods; Domain decomposition methods; Greens function; Helmholtz equations; Interpolation; Mathematical analysis; Mathematical domains; Mathematical models; Mathematical problems; Mathematics; Wavelengths
• ISSN: 0036-1429; 1095-7170
• DOI: 10.1137/130917144

We propose and study a domain decomposition method for solving the truncated perfectly matched layer (PML) approximation in bounded domain of Helmholtz scattering problems. The method is based on the decomposition of the domain into nonoverlapping layers and the idea of source transfer which transfers the sources equivalently layer by layer so that the solution in the final layer can be solved using a PML method defined locally outside the last two layers. The convergence of the method is proved for the case of constant wave number based on the analysis of the fundamental solution of the PML equation. The method can be used as an efficient preconditioner in the preconditioned GMRES method for solving discrete Helmholtz equations with constant and heterogeneous wave numbers. Numerical examples are included.