A fully discrete Calderón calculus for the two-dimensional elastic wave equation

Víctor Domínguez, Tonatiuh Sánchez-Vizuet, Francisco Javier Sayas

Research output: Contribution to journalArticlepeer-review

4 Scopus citations

Abstract

In this paper we present a full discretization of the layer potentials and boundary integral operators for the elastic wave equation on a parametrizable smooth closed curve in the plane. The method can be understood as a non-conforming Petrov-Galerkin discretization, with a very precise choice of testing functions by symmetrically combining elements on two staggered grids, and using a look-around quadrature formula. Unlike in the acoustic counterpart of this work, the kernel of the elastic double layer operator includes a periodic Hilbert transform that requires a particular choice of the mixing parameters. We give mathematical justification of this fact. Finally, we test the method on some frequency domain and time domain problems, and demonstrate its applicability on smooth open arcs.

Original languageEnglish (US)
Pages (from-to)620-635
Number of pages16
JournalComputers and Mathematics with Applications
Volume69
Issue number7
DOIs
StatePublished - Apr 1 2015
Externally publishedYes

Keywords

  • Calderón calculus
  • Elastic wave scattering
  • Time domain boundary integral equations

ASJC Scopus subject areas

  • Modeling and Simulation
  • Computational Theory and Mathematics
  • Computational Mathematics

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