SIAM Journal on Scientific Computing, Volume 42, Issue 4, Page A2014-A2036, January 2020.
In this paper we study elliptic partial differential equations with rapidly varying diffusion coefficient that can be represented as a perturbation of a reference coefficient. We develop a numerical method for efficiently solving multiple perturbed problems by reusing local computations performed with the reference coefficient. The proposed method is based on the Petrov--Galerkin localized orthogonal decomposition (PG-LOD), which allows for straightforward parallelization with low communication overhead and memory consumption. We focus on two types of perturbations: local defects, which we treat by recomputation of multiscale shape functions, and global mappings of a reference coefficient for which we apply the domain mapping method. We analyze the proposed method for these problem classes and present several numerical examples.

中文翻译：

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扰动扩散问题的数值放大

SIAM科学计算杂志，第42卷，第4期，第A2014-A2036页，2020年1月。
在本文中，我们研究扩散系数快速变化的椭圆型偏微分方程，该方程可以表示为参考系数的扰动。我们通过重用参考系数执行局部计算，开发了一种有效解决多个摄动问题的数值方法。所提出的方法基于Petrov-Galerkin局部正交分解（PG-LOD），可实现直接并行化，且通信开销和内存消耗低。我们关注两种类型的扰动：局部缺陷（通过多尺度形状函数的重新计算来处理）以及参考系数的全局映射（我们对其应用域映射方法）。我们分析针对这些问题类别的建议方法，并提供几个数值示例。