Symmetric Boundary-Finite Element Discretization of Time Dependent Acoustic Scattering by Elastic Obstacles with Piezoelectric Behavior

Tonatiuh Sánchez-Vizuet, Francisco Javier Sayas

Research output: Contribution to journalArticlepeer-review

8 Scopus citations

Abstract

A coupled BEM/FEM formulation for the transient interaction between an acoustic field and a piezoelectric scatterer is proposed. The scattered part of the acoustic wave is represented in terms of retarded layer potentials while the elastic displacement and electric potential are treated variationally. This results in an integro-differential system. Well posedness of a general Galerkin semi-discretization in space of the problem is shown in the Laplace domain and translated into explicit stability bounds in the time domain. Trapezoidal-rule and BDF2 convolution quadrature are used in combination with matching time stepping for time discretization. Second order convergence is proven for the BDF2-based method. Numerical experiments are provided for BDF2 and trapezoidal rule based time evolution.

Original languageEnglish (US)
Pages (from-to)1290-1315
Number of pages26
JournalJournal of Scientific Computing
Volume70
Issue number3
DOIs
StatePublished - Mar 1 2017
Externally publishedYes

Keywords

  • Convolution quadrature
  • Coupling BEM/FEM
  • Piezoelectricity
  • Scattering
  • Time-domain boundary integral equations

ASJC Scopus subject areas

  • Software
  • Theoretical Computer Science
  • Numerical Analysis
  • Engineering(all)
  • Computational Theory and Mathematics
  • Computational Mathematics
  • Applied Mathematics

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