Extending the method of fundamental solutions to non-homogeneous elastic wave problems

Carlos J.S. Alves, Nuno F.M. Martins, Svilen S. Valtchev

Research output: Contribution to journalArticlepeer-review

10 Citations (Scopus)

Abstract

Two meshfree methods are developed for the numerical solution of the non-homogeneous Cauchy–Navier equations of elastodynamics in an isotropic material. The two approaches differ upon the choice of the basis functions used for the approximation of the unknown wave amplitude. In the first case, the solution is approximated in terms of a linear combination of fundamental solutions of the Navier differential operator with different source points and test frequencies. In the second method the solution is approximated by superposition of acoustic waves, i.e. fundamental solutions of the Helmholtz operator, with different source points and test frequencies. The applicability of the two methods is justified in terms of density results and a convergence result is proven. The accuracy of the methods is illustrated through 2D numerical examples. Applications to interior elastic wave scattering problems are also presented.

Original languageEnglish
Pages (from-to)299-313
Number of pages15
JournalApplied Numerical Mathematics
Volume115
DOIs
Publication statusPublished - 1 May 2017

Keywords

  • Elastic wave scattering
  • Meshfree method
  • Method of fundamental solutions
  • Non-homogeneous problems

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