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An energy approach to space–time Galerkin BEM for wave propagation problems
Author(s) -
Aimi A.,
Diligenti M.,
Guardasoni C.,
Mazzieri I.,
Panizzi S.
Publication year - 2009
Publication title -
international journal for numerical methods in engineering
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.421
H-Index - 168
eISSN - 1097-0207
pISSN - 0029-5981
DOI - 10.1002/nme.2660
Subject(s) - galerkin method , bilinear interpolation , mathematics , boundary element method , bilinear form , space (punctuation) , stability (learning theory) , mathematical analysis , dirichlet distribution , integral equation , boundary value problem , finite element method , computer science , physics , statistics , machine learning , thermodynamics , operating system
Abstract In this paper we consider Dirichlet or Neumann wave propagation problems reformulated in terms of boundary integral equations with retarded potential. Starting from a natural energy identity, a space–time weak formulation for 1D integral problems is briefly introduced, and continuity and coerciveness properties of the related bilinear form are proved. Then, a theoretical analysis of an extension of the introduced formulation for 2D problems is proposed, pointing out the novelty with respect to existing literature results. At last, various numerical simulations will be presented and discussed, showing unconditional stability of the space–time Galerkin boundary element method applied to the energetic weak problem. Copyright © 2009 John Wiley & Sons, Ltd.