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.

翻译：本文提出了两种（解耦和耦合）基于积分方程的方法，用于求解外域中具有Neumann边界条件的Morse-Ingard方程。两种方法均基于第二类积分方程（SKIE）的构造。耦合方法具有良好的条件数，能够实现高精度。解耦方法计算成本较低，在处理边界层时具有更高的灵活性；但其解耦变换易出现病态问题，且无法达到与耦合方法相同的精度。我们通过基于扩展求积（QBX）的Nyström方法结合快速多极加速技术展示了数值算例，并验证了所提求解器在二维和三维复杂几何问题中的精度与效率。