Domain decomposition of stochastic PDEs: Theoretical formulations
Domain decomposition of stochastic PDEs: Theoretical formulations
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随机偏微分方程的域分解：理论公式
DOI：
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发表时间：
2009
期刊：
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通讯作者：
R. Ghanem
中科院分区：
文献类型：
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作者：
A. Sarkar;Nabil Benabbou;R. Ghanem
针对由随机偏微分方程定义的不确定系统，提出了一种新的区域分解理论框架。该方法包括几何空间中的区域分解方法和概率空间中的函数分解方法。概率分解基于随机有限元的一种形式，基于随机过程的正交分解和投影。空间分解通过基于Schur-补码的区域分解来实现。该方法旨在充分挖掘高性能计算平台的潜力，通过高分辨率数值模式减少离散化误差，并适当考虑系统中的不确定性。以随机介质中的波为例，对数学公式进行了数值验证。版权所有©2008 John Wiley&Sons，Ltd.
We present a novel theoretical framework for the domain decomposition of uncertain systems defined by stochastic partial differential equations. The methodology involves a domain decomposition method in the geometric space and a functional decomposition in the probabilistic space. The probabilistic decomposition is based on a version of stochastic finite elements based on orthogonal decompositions and projections of stochastic processes. The spatial decomposition is achieved through a Schur‐complement‐based domain decomposition. The methodology aims to exploit the full potential of high‐performance computing platforms by reducing discretization errors with high‐resolution numerical model in conjunction to giving due regards to uncertainty in the system. The mathematical formulation is numerically validated with an example of waves in random media. Copyright © 2008 John Wiley & Sons, Ltd.