论文标题
PDE的空间和混乱 - 膨胀Galerkin POD低阶离散化用于不确定性定量
Space and Chaos-Expansion Galerkin POD Low-order Discretization of PDEs for Uncertainty Quantification
论文作者
论文摘要
除非采取适当的措施来降低模型的复杂性，否则部分微分方程中多元不确定性的量化很容易超越任何计算能力。在这项工作中，我们提出了一个多维盖尔金适当的正交分解，可最佳地降低张张量的产品空间的每个维度。我们提供分析框架和定义低维近似的结果。我们说明了其用于多项式混乱扩展的不确定性建模的应用，并在数值示例中显示了其效率。
The quantification of multivariate uncertainties in partial differential equations can easily exceed any computing capacity unless proper measures are taken to reduce the complexity of the model. In this work, we propose a multidimensional Galerkin Proper Orthogonal Decomposition that optimally reduces each dimension of a tensorized product space. We provide the analytical framework and results that define and quantify the low-dimensional approximation. We illustrate its application for uncertainty modeling with Polynomial Chaos Expansions and show its efficiency in a numerical example.
