Nonreflecting boundary condition for the Helmholtz equation
| Autor: | A.S. Deakin, H. Rasmussen |
|---|---|
| Rok vydání: | 2001 |
| Předmět: |
Helmholtz equation
Exact boundary conditions Mathematical analysis Mixed boundary condition 01 natural sciences Poincaré–Steklov operator Robin boundary condition 010305 fluids & plasmas 010101 applied mathematics symbols.namesake Computational Mathematics Computational Theory and Mathematics Modeling and Simulation Dirichlet boundary condition Modelling and Simulation 0103 physical sciences symbols Neumann boundary condition Cauchy boundary condition Boundary value problem 0101 mathematics Acoustic scattering Mathematics |
| Zdroj: | Computers & Mathematics with Applications. 41(3-4):307-318 |
| ISSN: | 0898-1221 |
| DOI: | 10.1016/s0898-1221(00)00275-3 |
| Popis: | To solve the Helmholtz equation in an infinite three-dimensional domain a spherical artificial boundary is introduced to restrict the computational domain Ω. To determine the nonreflecting boundary condition on ∂Ω, we start with a finite number of spherical harmonics for the Helmholtz equation. With a precise choice of (primary) nodes on the sphere, the theorem on Gauss-Jordan quadrature establishes the discrete orthogonality of the spherical harmonics when summed over these nodes. An approximate nonreflecting boundary condition for the Helmholtz equation follows readily upon solving the exterior Dirichlet problem. The accuracy of the boundary condition is determined using a point source, and the computational results are presented for the scattering of a wave from a sphere. |
| Databáze: | OpenAIRE |
| Externí odkaz: |
|
Full Text from ScienceDirect