Integral Equation Formulation of the Biharmonic Dirichlet Problem

M. Rachh, T. Askham

Research output: Contribution to journalArticlepeer-review

6 Scopus citations

Abstract

We present a novel integral representation for the biharmonic Dirichlet problem. To obtain the representation, the Dirichlet problem is first converted into a related Stokes problem for which the Sherman–Lauricella integral representation can be used. Not all potentials for the Dirichlet problem correspond to a potential for Stokes flow, and vice-versa, but we show that the integral representation can be augmented and modified to handle either simply or multiply connected domains. The resulting integral representation has a kernel which behaves better on domains with high curvature than existing representations. Thus, this representation results in more robust computational methods for the solution of the Dirichlet problem of the biharmonic equation and we demonstrate this with several numerical examples.

Original languageEnglish (US)
Pages (from-to)762-781
Number of pages20
JournalJournal of Scientific Computing
Volume75
Issue number2
DOIs
StatePublished - May 1 2018
Externally publishedYes

All Science Journal Classification (ASJC) codes

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

Keywords

  • Biharmonic
  • Dirichlet
  • Integral equations
  • Multiply connected

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