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An elastodynamic Galerkin Boundary Element Formulation for semi‐infinite domains in time‐domain
Author(s) -
Kielhorn Lars,
Schanz Martin
Publication year - 2008
Publication title -
pamm
Language(s) - English
Resource type - Journals
ISSN - 1617-7061
DOI - 10.1002/pamm.200810295
Subject(s) - galerkin method , discretization , boundary element method , mathematics , bilinear form , bilinear interpolation , mathematical analysis , regularization (linguistics) , boundary (topology) , domain (mathematical analysis) , element (criminal law) , finite element method , computer science , physics , artificial intelligence , political science , law , thermodynamics , statistics
The present work focuses on the problem of modelling wave propagation phenomena within a 3–d elastodynamic halfspace by use of a symmetric Galerkin Boundary Element formulation. Unfortunately, this formulation requires the evaluation of hypersingular integral kernels which are regularized by integration by parts. In Boundary Element Methods semi–infinite domains are commonly approximated in space by considering just a sufficiently large enough region. Applying this simple discretization to the symmetric formulation implies the evaluation of the hypersingular bilinear form on a truncated mesh which will fail due to the regularization approach. To overcome this drawback a methodology based on infinite elements is presented. The numerical tests show that this approach is promising for treating semi–infinite domains with a symmetric Galerkin scheme. (© 2008 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)