标题： 指数型非均匀气体中的声学奇异曲面：一种基于Krylov子空间谱方法的新数值方法 显示英文标题

标题： Acoustic singular surfaces in an exponential class of inhomogeneous gases: A new numerical approach based on Krylov subspace spectral methodologies

摘要： 我们研究声学奇异面的传播，具体来说，是线性冲击波和非线性加速波在一类环境质量密度呈指数变化的非均匀气体中的传播。 利用奇异面理论的数学工具，我们首先确定了跃迁振幅以及相关波前的位置/速度的演变，以及一系列相关的分析结果。 随后，我们转向被称为基里洛夫子空间谱（KSS）方法的数值模拟，以模拟所考虑的完整波形的演变。 这些方法不仅执行得非常高效，因为KSS允许使用“大”CFL数，而且在捕捉理论上预测的解轮廓特征方面比其他时间步进方法更加精确，因为KSS会针对涉及的不同频率对应的解的组成部分进行定制计算。 最后，我们列出了一些可能的与声学相关的后续研究。 显示英文摘要

摘要： We investigate the propagation of acoustic singular surfaces, specifically, linear shock waves and nonlinear acceleration waves, in a class of inhomogeneous gases whose ambient mass density varies exponentially. Employing the mathematical tools of singular surface theory, we first determine the evolution of both the jump amplitudes and the locations/velocities of their associated wave-fronts, along with a variety of related analytical results. We then turn to what have become known as Krylov subspace spectral (KSS) methods to numerically simulate the evolution of the full waveforms under consideration. These are not only performed quite efficiently, since KSS allows the use of `large' CFL numbers, but also quite accurately, in the sense of capturing theoretically-predicted features of the solution profiles more faithfully than other time-stepping methods, since KSS customizes the computation of the components of the solution corresponding to the different frequencies involved. The presentation concludes with a listing of possible, acoustics-related, follow-on studies.