论文标题
Morse-Indard方程的确切域截断
Exact domain truncation for the Morse-Ingard equations
论文作者
论文摘要
Morse和Ingard为激发气体的温度和压力提供了耦合的时谐度方程系统。这些方程构成了建模痕量气体传感器的关键方面。像其他波浪传播问题一样，计算问题必须在合适的远场边界条件下封闭。我们在散射的场公式中工作，我们适应了赫尔姆霍尔兹方程前提出的非本地边界条件，以适应该耦合系统。该边界条件使用绿色的公式用于边界上的真实解决方案，从而导致标准传输边界条件的非本地扰动。但是，边界条件是精确的，因此所产生问题的盖尔金离散化收敛到精确解决方案对计算域的限制。数值结果表明，可以在小型计算域上的相对粗糙的网格上获得准确性，并且可以使用操作员的局部部分作为有效的预处理程序来通过GMRE求解所得的代数系统。
Morse and Ingard give a coupled system of time-harmonic equations for the temperature and pressure of an excited gas. These equations form a critical aspect of modeling trace gas sensors. Like other wave propagation problems, the computational problem must be closed with suitable far-field boundary conditions. Working in a scattered-field formulation, we adapt a nonlocal boundary condition proposed earlier for the Helmholtz equation to this coupled system. This boundary condition uses a Green's formula for the true solution on the boundary, giving rise to a nonlocal perturbation of standard transmission boundary conditions. However, the boundary condition is exact and so Galerkin discretization of the resulting problem converges to the restriction of the exact solution to the computational domain. Numerical results demonstrate that accuracy can be obtained on relatively coarse meshes on small computational domains, and the resulting algebraic systems may be solved by GMRES using the local part of the operator as an effective preconditioner.
