Well-conditioned boundary integral equation formulations and nyström discretizations for the solution of Helmholtz problems with impedance boundary conditions in two-dimensional Lipschitz domains

Catalin Turc, Yassine Boubendir, Mohamed Kamel Riahi

Research output: Contribution to journalArticlepeer-review

4 Scopus citations

Abstract

We present a regularization strategy that leads to well-conditioned boundary integral equation formulations of Helmholtz equations with impedance boundary conditions in two-dimensional Lipschitz domains. We consider both the case of classical impedance boundary conditions, as well as that of transmission impedance conditions wherein the impedances are certain coercive operators. The latter type of problem is instrumental in the speed up of the convergence of Domain Decomposition Methods for Helmholtz problems. Our regularized formulations use as unknowns the Dirichlet traces of the solution on the boundary of the domain. Taking advantage of the increased regularity of the unknowns in our formulations, we show through a variety of numerical results that a graded-mesh based Nyström discretization of these regularized formulations leads to efficient and accurate solutions of interior and exterior Helmholtz problems with impedance boundary conditions.

Original languageEnglish (US)
Pages (from-to)441-472
Number of pages32
JournalJournal of Integral Equations and Applications
Volume29
Issue number3
DOIs
StatePublished - 2017

All Science Journal Classification (ASJC) codes

  • Numerical Analysis
  • Applied Mathematics

Keywords

  • Graded meshes
  • Impedance boundary value problems
  • Integral equations
  • Lipschitz domains
  • Nyström method
  • Regularizing operators

Fingerprint Dive into the research topics of 'Well-conditioned boundary integral equation formulations and nyström discretizations for the solution of Helmholtz problems with impedance boundary conditions in two-dimensional Lipschitz domains'. Together they form a unique fingerprint.

Cite this