A fast discrete spectral method for stochastic partial differential equations
A fast discrete spectral method for stochastic partial differential equations
复制标题
随机偏微分方程的快速离散谱方法
DOI：
10.1007/s10444-017-9513-4
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发表时间：
2017
影响因子：
1.7
通讯作者：
许跃生
中科院分区：
文献类型：
--
作者：
曹延昭;江颖;许跃生
本文的目的是构造一个有效的数值算法来计算由随机椭圆型偏微分方程的谱伽辽金近似引起的线性系统的系数矩阵和右侧。我们证明了所提出的算法只需要n次算术运算即可达到指数收敛，其中d+1是算法中使用的一维正交多项式的最高次，d+1是有限karhunen - losamade （K-L）展开中的项数。数值实验验证了该算法的理论估计和计算效率。
The goal of this paper is to construct an efficient numerical algorithm for computing the coefficient matrix and the right hand side of the linear system resulting from the spectral Galerkin approximation of a stochastic elliptic partial differential equation. We establish that the proposed algorithm achieves an exponential convergence with requiring only Onumber of arithmetic operations, wherenis the highest degree of the one dimensional orthogonal polynomial used in the algorithm,d+1 is the number of terms in the finite Karhunen–Loéve (K-L) expansion. Numerical experiments confirm the theoretical estimates of the proposed algorithm and demonstrate its computational efficiency.