Finite Elements for Helmholtz Equations with a Nonlocal Boundary Condition
| Autor: | Ben Sepanski, Andreas Klöckner, Robert C. Kirby |
|---|---|
| Rok vydání: | 2021 |
| Předmět: |
Helmholtz equation
Truncation Applied Mathematics Numerical resolution Mathematical analysis Nonlocal boundary Numerical Analysis (math.NA) 010103 numerical & computational mathematics 01 natural sciences Domain (mathematical analysis) Finite element method 65N30 65N80 65F08 Computational Mathematics symbols.namesake Helmholtz free energy FOS: Mathematics symbols Mathematics - Numerical Analysis Boundary value problem 0101 mathematics Mathematics |
| Zdroj: | SIAM Journal on Scientific Computing. 43:A1671-A1691 |
| ISSN: | 1095-7197 1064-8275 |
| DOI: | 10.1137/20m1368100 |
| Popis: | Numerical resolution of exterior Helmholtz problems requires some approach to domain truncation. As an alternative to approximate nonreflecting boundary conditions and invocation of the Dirichlet-to-Neumann map, we introduce a new, nonlocal boundary condition. This condition is exact and requires the evaluation of layer potentials involving the free space Green's function. However, it seems to work in general unstructured geometry, and Galerkin finite element discretization leads to convergence under the usual mesh constraints imposed by G{\aa}rding-type inequalities. The nonlocal boundary conditions are readily approximated by fast multipole methods, and the resulting linear system can be preconditioned by the purely local operator involving transmission boundary conditions. |
| Databáze: | OpenAIRE |
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