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A stochastic collocation approach for parabolic PDEs with random domain deformations
Computers & Mathematics with Applications ( IF 2.9 ) Pub Date : 2021-04-15 , DOI: 10.1016/j.camwa.2021.04.005
Julio E Castrillón-Candás 1 , Jie Xu 1
Affiliation  

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.



中文翻译:

具有随机域变形的抛物线偏微分方程的随机搭配方法

在本文中,我们分析了具有随机域变形的线性抛物型偏微分方程。特别是,我们专注于数值近似给定感兴趣数量 (QoI) 的统计矩的问题。几何形状被假定为随机的。抛物线问题被重新映射到具有随机系数的固定确定域,并显示允许在嵌入复杂超平面的明确区域上进行扩展。QoI 的随机矩是通过采用搭配方法与各向同性 Smolyak 稀疏网格相结合来计算的。推导出作为搭配插值节点数量的函数的理论次指数收敛速度。进行了数值实验,它们证实了理论误差估计。

更新日期:2021-04-16
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