03-22
On the boundary conditions for EG-methods applied to the two-dimensional wave equation system
by Lukacova-Medvidova, M.; Warnecke, G.; Zahaykah, Y.
Preprint series: 03-22, Preprints
- MSC:
- 35L05 Wave equation
- 65M06 Finite difference methods
Abstract: The subjekt of the paper is the study of some nonreflecting and reflecting boundary conditions for the evolution Galerkin methods (EG) which are applied for the two-dimensional wave equation system. Different tools are used to achieve this aim. Namely, the method of characteristics, the method of extrapolation, the Laplace transformation method, and the perfectly matched layer (PML) method. We show that the absorbing boundary conditions which are based on the use of the Laplace transformation lead to the Engquist-Majda first and second order absorbing boundary conditions, see (2). Further, following Berenger (1) we give the PML analysis. We discretize the wave equation system with the leap-frog scheme inside the PML while the evolution Galerkin schemes are used inside the computational domain. Numerical tests demonstrate that this method produces no unphysical reflected waves as well as the best results in comparison with other techniques studied in the paper.
Keywords: hyperbolic systems, wave equation, evolution Galerkin schemes, absorbing boundary conditions, reflecting boundary conditions, perfectly matched layer, Laplace transformation.
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