具有随机域变形的抛物线 PDE 的随机搭配方法。A stochastic collocation approach for parabolic PDEs with random domain deformations.-医云文献数字医云科研云海量医学决策数据服务

Abstract：

In this article we analyze the linear parabolic partial differential equation with a stochastic domain deformation. In particular, we concentrate on the problem of numerically approximating the statistical moments of a given Quantity of Interest (QoI). The geometry is assumed to be random. The parabolic problem is remapped to a fixed deterministic domain with random coefficients and shown to admit an extension on a well defined region embedded in the complex hyperplane. The stochastic moments of the QoI are computed by employing a collocation method in conjunction with an isotropic Smolyak sparse grid. Theoretical sub-exponential convergence rates as a function to the number of collocation interpolation knots are derived. Numerical experiments are performed and they confirm the theoretical error estimates.

摘要：

在本文中，我们分析了具有随机域变形的线性抛物线偏微分方程。特别是,我们专注于数值逼近给定兴趣量(QoI)的统计矩的问题。假定几何形状是随机的。抛物线问题被重新映射到具有随机系数的固定确定性域，并显示允许在嵌入复杂超平面的定义明确的区域上进行扩展。QoI的随机矩是通过采用搭配方法结合各向同性Smolyak稀疏网格来计算的。推导了理论上的子指数收敛率，它是搭配插值节数的函数。进行了数值实验，并证实了理论误差估计。