Integral equation methods for the Morse-Ingard equations

Xiaoyu Wei, Andreas Klöckner, Robert C. Kirby

Research output: Contribution to journalArticlepeer-review


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
StatePublished - Nov 1 2023


  • 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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