Integral equation methods for the Morse-Ingard equations

Xiaoyu Wei, Andreas Klöckner, Robert C. Kirby

Research output: Contribution to journalArticlepeer-review

Abstract

We present two (a decoupled and a coupled) integral-equation-based methods for the Morse-Ingard equations subject to Neumann boundary conditions on the exterior domain. Both methods are based on second-kind integral equation (SKIE) formulations. The coupled method is well-conditioned and can achieve high accuracy. The decoupled method has lower computational cost and more flexibility in dealing with the boundary layer; however, it is prone to the ill-conditioning of the decoupling transform and cannot achieve as high accuracy as the coupled method. We show numerical examples using a Nyström method based on quadrature-by-expansion (QBX) with fast-multipole acceleration. We demonstrate the accuracy and efficiency of the solvers in both two and three dimensions with complex geometry.

Original languageEnglish (US)
Article number112416
JournalJournal of Computational Physics
Volume492
DOIs
StatePublished - Nov 1 2023

Keywords

  • Fast multipole method
  • Integral equation method
  • Quadrature-by-expansion
  • The Morse-Ingard equations

ASJC Scopus subject areas

  • Numerical Analysis
  • Modeling and Simulation
  • Physics and Astronomy (miscellaneous)
  • General Physics and Astronomy
  • Computer Science Applications
  • Computational Mathematics
  • Applied Mathematics

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