Coupling at a distance HDG and BEM

Bernardo Cockburn, Francisco Javier Sayas, Manuel Solano

Research output: Contribution to journalArticlepeer-review

8 Scopus citations

Abstract

We introduce a new technique for numerically solving exterior Dirichlet boundaryvalue problems for second-order elliptic equations. It consists of coupling a hybridizable discontinuous Galerkin (HDG) method used for solving the so-called interior problem on a bounded region containing the support of the source term, with a boundary element method (BEM) for solving the problem exterior to that region. The novelty is that the BEM is defined on a suitably chosen, smooth artificial boundary whereas the HDG method is defined on a polyhedral subdomain. Because of the choice of the artificial boundary, we can take advantage of the spectral convergence of the BEM solution and of the simplicity of the corresponding equations. Because the HDG method is defined on a polyhedral subdomain, there is no need to try to fit the mesh to the artificial boundary. Instead, the HDG is coupled at a distance with the BEM by using simple Dirichlet-to-Neumann operators defined in the region between the artificial boundary and the polyhedral subdomain. Numerical experiments displaying the performance of the new technique are presented. Optimal orders of convergence are obtained even though the distance between the artificial boundary and the polyhedral domain is of order h.

Original languageEnglish (US)
JournalSIAM Journal on Scientific Computing
Volume34
Issue number1
DOIs
StatePublished - May 28 2012

Keywords

  • Boundary element methods
  • Coupling
  • Curved domains
  • Discontinuous Galerkin methods

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