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On the boundary conditions for EG methods applied to the two‐dimensional wave equation system
Author(s) -
LukáčováMedvid'ová M.,
Warnecke G.,
Zahaykah Y.
Publication year - 2004
Publication title -
zamm ‐ journal of applied mathematics and mechanics / zeitschrift für angewandte mathematik und mechanik
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.449
H-Index - 51
eISSN - 1521-4001
pISSN - 0044-2267
DOI - 10.1002/zamm.200310103
Subject(s) - discretization , laplace transform , extrapolation , galerkin method , mathematics , boundary value problem , mathematical analysis , transformation (genetics) , perfectly matched layer , boundary (topology) , laplace's equation , wave equation , domain (mathematical analysis) , finite element method , physics , biochemistry , chemistry , gene , thermodynamics
The subject of the paper is the study of several nonreflecting and reflecting boundary conditions for the evolution Galerkin (EG) methods which are applied for the two‐dimensional wave equation system. Different known 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 [3]. Further, following Bérenger [1] we consider the PML method. 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 much less unphysical reflected waves as well as the best results in comparison with other techniques studied in the paper.