The Morse–Ingard equations of thermoacoustics Morse and Ingard (1986) are a system of coupled time-harmonic equations for the temperature and pressure of an excited gas. They form a critical aspect of modeling trace gas sensors. In this paper, we analyze a reformulation of the system that has a weaker coupling between the equations than the original form. We give a Gårding-type inequality for the system that leads to optimal-order asymptotic finite element error estimates. We also develop preconditioners for the coupled system. These are derived by writing the system as a 2 × 2 block system with pressure and temperature unknowns segregated into separate blocks and then using either the block diagonal or block lower triangular part of this matrix as a preconditioner. Consequently, the preconditioner requires inverting smaller, Helmholtz-like systems individually for the pressure and temperature. Rigorous eigenvalue bounds are given for the preconditioned system, and these are supported by numerical experiments.

热声学的Morse-Ingard方程式Morse和Ingard（1986）是一种用于激发气体的温度和压力的耦合时谐方程组。它们构成了对痕量气体传感器进行建模的关键方面。在本文中，我们分析了方程组之间的耦合度比原始形式弱的系统重构形式。我们给出了导致最佳阶渐近有限元误差估计的系统的Gårding型不等式。我们还为耦合系统开发了预处理器。这些是通过将系统写为2×2块系统而得出的，其中压力和温度未知数被隔离到单独的块中，然后使用该矩阵的块对角线或块下三角部分作为前置条件。因此，前置调节器需要反转较小的 类亥姆霍兹系统分别用于压力和温度。给出了预处理系统的严格特征值范围，并通过数值实验对其进行了支持。