论文标题
减少了具有随机输入的部分微分方程的基础随机galerkin方法
Reduced basis stochastic Galerkin methods for partial differential equations with random inputs
论文作者
论文摘要
我们为具有随机输入的部分微分方程提供了降低的基础随机盖金方法。在这种方法中，减少的基础方法被整合到随机的Galerkin方法中，从而大大降低了解决Galerkin系统的成本。为了减少与我们减少的基础随机盖尔金方法有关的矩阵矢量操纵的主要成本，应用了SECANT方法来确定降低的基础功能的数量。我们提出了该方法的一般数学框架，验证其准确性并通过数值实验证明其效率。
We present a reduced basis stochastic Galerkin method for partial differential equations with random inputs. In this method, the reduced basis methodology is integrated into the stochastic Galerkin method, resulting in a significant reduction in the cost of solving the Galerkin system. To reduce the main cost of matrix-vector manipulation involved in our reduced basis stochastic Galerkin approach, the secant method is applied to identify the number of reduced basis functions. We present a general mathematical framework of the methodology, validate its accuracy and demonstrate its efficiency with numerical experiments.
