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arXiv · 1908.00652

Numerical upscaling of perturbed diffusion problems

Fredrik Hellman·Tim Keil·Axel Målqvist
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Abstract

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 communcation 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.

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Fredrik Hellman, Tim Keil, Axel Målqvist. 2019-08-01. Numerical upscaling of perturbed diffusion problems. https://doi.org/10.1137/19m1278211

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