Abstract Basis adaptation and domain decomposition for steady-state partial differential equations with random coefficients
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Basis adaptation and domain decomposition for steady-state partial differential equations with random coefficients

机译：随机系数的稳态偏微分方程的基础适应与域分解

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AbstractWe present a novel approach for solving steady-state stochastic partial differential equations in high-dimensional random parameter space. The proposed approach combines spatial domain decomposition with basis adaptation for each subdomain. The basis adaptation is used to address the curse of dimensionality by constructing an accurate low-dimensional representation of the stochastic PDE solution (probability density function and/or its leading statistical moments) in each subdomain. Restricting the basis adaptation to a specific subdomain affords finding a locally accurate solution. Then, the solutions from all of the subdomains are stitched together to provide a global solution. We support our construction with numerical experiments for a steady-state diffusion equation with a random spatially dependent coefficient. Our results show that accurate global solutions can be obtained with significantly reduced computational costs.]]>
机译：摘要“>我们提出了一种在高维随机参数空间中求解稳态随机偏微分方程的新方法。该方法将空间域分解与每个子域的基自适应相结合。基自适应通过构造随机偏微分方程解的精确低维表示来解决维数灾难n（概率密度函数和/或其领先统计矩）在每个子域中。将基自适应限制到特定子域，可以找到局部精确的解决方案。然后，将所有子域的解缝合在一起，以提供全局解。我们通过数值实验支持我们对一个具有随机空间相关系数的稳态扩散方程的构造。我们的结果表明，可以获得精确的全局解，并显著降低计算成本]>

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