论文标题
用于异质随机培养基中波传播的准蒙特卡洛有限元分析
Quasi-Monte Carlo finite element analysis for wave propagation in heterogeneous random media
论文作者
论文摘要
我们提出和分析了准蒙特卡洛（QMC）算法，以有效地模拟由Helmholtz方程建模的波传播，在界面区域中，折射率是随机的，在空间上是异质的。我们的重点是该区域可以包含多个波长的情况。我们通过切换到Ganesh and Morgenstern最近开发的替代标志定式配方（数字算法，83，1441-1487，2020），绕过了Helmholtz问题的通常标志性分离性。付款的代价是，QMC方法所需的规律性分析变得更加技术性。然而，我们获得了一个完整的分析，其中包含随机维度截断误差，有限元误差和立方体误差，其结果与扩散问题获得的结果相当。
We propose and analyze a quasi-Monte Carlo (QMC) algorithm for efficient simulation of wave propagation modeled by the Helmholtz equation in a bounded region in which the refractive index is random and spatially heterogenous. Our focus is on the case in which the region can contain multiple wavelengths. We bypass the usual sign-indefiniteness of the Helmholtz problem by switching to an alternative sign-definite formulation recently developed by Ganesh and Morgenstern (Numerical Algorithms, 83, 1441-1487, 2020). The price to pay is that the regularity analysis required for QMC methods becomes much more technical. Nevertheless we obtain a complete analysis with error comprising stochastic dimension truncation error, finite element error and cubature error, with results comparable to those obtained for the diffusion problem.
