Integral equation methods for the Morse-ingard equations. (English) Zbl 07742902
Summary: 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.
MSC:
| 35Jxx | Elliptic equations and elliptic systems |
| 65Dxx | Numerical approximation and computational geometry (primarily algorithms) |
| 65Rxx | Numerical methods for integral equations, integral transforms |
Keywords:
Morse-Ingard equations; fast multipole method; integral equation method; quadrature-by-expansionSoftware:
DLMFReferences:
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