Neumann exterior wave propagation problems: computational aspects of 3D energetic Galerkin BEM

Authors:
A. Aimi;M. Diligenti;A. Frangi;C. Guardasoni
Affiliations:
Department of Mathematics, Università di Parma, Parma, Italy 43124;Department of Mathematics, Università di Parma, Parma, Italy 43124;Department of Structural Engineering, Politecnico di Milano, Milano, Italy 20133;Department of Mathematics, Università di Parma, Parma, Italy 43124
Venue:
Computational Mechanics
Year:
2013

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Abstract

In this work, we consider as model problem an exterior 3D wave propagation Neumann problem reformulated in terms of a space---time hypersingular boundary integral equation with retarded potentials. This latter is set in the so-called energetic weak form, recently proposed in Aimi et al. (Int J Numer Methods Eng 80:1196---1240, 2009; CMES 58:185---219, 2010), regularized as in Frangi (Int J Numer Methods Eng 45:721---740, 1999) and then approximated by the Galerkin boundary element method. Details on the discretization phase and, in particular, on the computation of integrals, double in time and double in space, constituting the elements of the final linear system matrix are given and analyzed. Various numerical results and simulations are presented and discussed.