.png){kind=icon}
返回
Stochastic domain decomposition based on variable-separation method
.png){kind=icon}
OA
AI
DOI：10.1016/j.cma.2023.116538.png)
.png){kind=icon}
.png){kind=icon}
分享.png){kind=icon}
收藏
摘要
En 中文
This work proposes a stochastic domain decomposition method for solving steady-state partial differential equations (PDEs) with random inputs. Specifically, based on the efficiency of the variable-separation (VS) method in simulating stochastic partial differential equations (SPDEs), we extend it to stochastic algebraic systems and employ it in the context of stochastic domain decomposition. The resulting method, termed stochastic domain decomposition based on variable-separation (SDD-VS) alleviates the challenge commonly known as the curse of dimensionalitynotably by leveraging explicit representations of stochastic functions derived from physical systems. The primary objective of the proposed SDD-VS method is to obtain a separate representation of the solution for the stochastic interface problem. To enhance computational efficiency, we introduce a two-phase approach consisting of offline and online computation. In the offline phase, we establish an affine representation of stochastic algebraic systems by systematically applying the VS method. During the online phase, we estimate the interface unknowns of SPDEs using a quasi-optimal separated representation, facilitating the construction of efficient surrogate models for subproblems. We substantiate the effectiveness of our proposed approach through numerical experiments involving three specific instances, demonstrating its capability to provide accurate solutions.
Keyword:
Stochastic partial differential equation
Stochastic domain decomposition
Stochastic interface problem
Variable-separation method
Uncertainty quantification
AI总结
对已上传原文的论文进行重点信息的提取，主要内容包括：简要概述、研究摘要、背景介绍、关键亮点、图文解析、展望与总结。
期刊
IF:
7.3
论文数:
1.3W
被引数:
5.6W
机构
引用论文
.png){kind=icon}
分享收藏分享收藏A new era in scientific computing: Domain decomposition methods in hybrid CPU-GPU architectures科学计算的新时代: 混合cpu-gpu架构中的域分解方法
PREAI
分享收藏
查看更多内容