2021/03/22 by Evan North, North, Evan, Semyon Tsynkov +3
Engineering · Physics and Astronomy · #Electromagnetic Scattering and Analysis #Electromagnetic Simulation and Numerical Methods #FOS: Mathematics #Numerical Analysis (math.NA) #Numerical methods in engineering
paper · pdf · doi:10.48550/arxiv.2103.12172
openalex publication_date 2021/03/22 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
We use the Method of Difference Potentials (MDP) to solve a non-overlapping\ndomain decomposition formulation of the Helmholtz equation. The MDP reduces the\nHelmholtz equation on each subdomain to a Calderon's boundary equation with\nprojection on its boundary. The unknowns for the Calderon's equation are the\nDirichlet and Neumann data. Coupling between neighboring subdomains is rendered\nby applying their respective Calderon's equations to the same data at the\ncommon interface. Solutions on individual subdomains are computed concurrently\nusing a straightforward direct solver. We provide numerical examples\ndemonstrating that our method is insensitive to interior cross-points and mixed\nboundary conditions, as well as large jumps in the wavenumber for transmission\nproblems, which are known to be problematic for many other Domain Decomposition\nMethods.\n