Absorbing boundaries for wave propagation problems. (English) Zbl 0644.65086
Reflections or wraparound from boundaries of numerical grids have always presented a difficulty in applying discrete methods to simulate physical phenomena. This study presents a systematic derivation of absorbing boundary conditions which can be used in a wide class of wave equations. The derivation is applied to the Schrödinger equations and to the acoustic equation in one and two dimensions. The effectiveness of the absorbing boundary conditions can be evaluated apriori on the basis of analytic solutions.
MSC:
| 65Z05 | Applications to the sciences |
| 65N50 | Mesh generation, refinement, and adaptive methods for boundary value problems involving PDEs |
| 35L05 | Wave equation |
| 35Q99 | Partial differential equations of mathematical physics and other areas of application |
| 76Q05 | Hydro- and aero-acoustics |
| 81Q05 | Closed and approximate solutions to the Schrödinger, Dirac, Klein-Gordon and other equations of quantum mechanics |
Keywords:
numerical simulation of wave propagation; numerical grids; absorbing boundary conditions; wave equations; Schrödinger equations; acoustic equationReferences:
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