2020/02/13 by Wei Leng, Lili Ju, Leng, Wei +1
Engineering · Physics and Astronomy · #Advanced Numerical Methods in Computational Mathematics #Electromagnetic Scattering and Analysis #Electromagnetic Simulation and Numerical Methods #FOS: Mathematics #Numerical Analysis (math.NA)
paper · pdf · doi:10.48550/arxiv.2002.05327
openalex publication_date 2020/02/13 · openalex created_date 2020/02/24 · openalex updated_date 2026/07/28
In this paper, we propose and test a novel diagonal sweeping domain decomposition method (DDM) with source transfer for solving the high-frequency Helmholtz equation in ℝn. In the method the computational domain is partitioned into overlapping checkerboard subdomains for source transfer with the perfectly matched layer (PML) technique, then a set of diagonal sweeps over the subdomains are specially designed to solve the system efficiently. The method improves the additive overlapping DDM (W. Leng and L. Ju, 2019) and the L-sweeps method (M. Taus, et al., 2019) by employing a more efficient subdomain solving order. We show that the method achieves the exact solution of the global PML problem with 2n sweeps in the constant medium case. Although the sweeping usually implies sequential subdomain solves, the number of sequential steps required for each sweep in the method is only proportional to the n-th root of the number of subdomains when the domain decomposition is quasi-uniform with respect to all directions, thus it is very suitable for parallel computing of the Helmholtz problem with multiple right-hand sides through the pipeline processing. Extensive numerical experiments in two and three dimensions are presented to demonstrate the effectiveness and efficiency of the proposed method.