Efficient Adaptive Stochastic Collocation Strategies for Advection-Diffusion Problems with Uncertain Inputs
Efficient Adaptive Stochastic Collocation Strategies for Advection-Diffusion Problems with Uncertain Inputs
复制标题
具有不确定输入的平流扩散问题的高效自适应随机配置策略
DOI：
10.1007/s10915-023-02247-w
复制
发表时间：
2023
影响因子：
2.5
通讯作者：
Kent B
中科院分区：
文献类型：
--
作者：
Kent B
具有不确定输入的物理模型通常表示为参数偏微分方程（PDE）。也就是说，偏微分方程的输入被表示为具有相关概率分布的参数的函数。开发同时考虑空间、时间和参数域上的误差的高效且准确的解决方案策略是极具挑战性的。事实上，众所周知，参数域上的标准多项式近似会引起随时间增长的误差。在这项工作中，我们专注于对流扩散问题与参数依赖的风场。提出了一种新的自适应解决方案，允许用户结合联合收割机随机配置的参数域与现成的自适应时间步长算法与本地错误控制。这是一种非侵入式策略，它构建了一个基于多项式的代理，该代理在时间上按顺序进行调整。该算法是由一个所谓的分层估计的参数误差和平衡这对全球时间步长误差的估计，这是来自一个缩放参数。
Physical models with uncertain inputs are commonly represented as parametric partial differential equations (PDEs). That is, PDEs with inputs that are expressed as functions of parameters with an associated probability distribution. Developing efficient and accurate solution strategies that account for errors on the space, time and parameter domains simultaneously is highly challenging. Indeed, it is well known that standard polynomial-based approximations on the parameter domain can incur errors that grow in time. In this work, we focus on advection–diffusion problems with parameter-dependent wind fields. A novel adaptive solution strategy is proposed that allows users to combine stochastic collocation on the parameter domain with off-the-shelf adaptive timestepping algorithms with local error control. This is a non-intrusive strategy that builds a polynomial-based surrogate that is adapted sequentially in time. The algorithm is driven by a so-called hierarchical estimator for the parametric error and balances this against an estimate for the global timestepping error which is derived from a scaling argument.