Integral Equation Methods for the Morse-Ingard Equations
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 Nystr\"om 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.
Cite
@article{arxiv.2210.12542,
title = {Integral Equation Methods for the Morse-Ingard Equations},
author = {Xiaoyu Wei and Andreas Klöckner and Robert C. Kirby},
journal= {arXiv preprint arXiv:2210.12542},
year = {2023}
}