Numerical upscaling of perturbed diffusion problems
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.
Cite
@article{arxiv.1908.00652,
title = {Numerical upscaling of perturbed diffusion problems},
author = {Fredrik Hellman and Tim Keil and Axel Målqvist},
journal= {arXiv preprint arXiv:1908.00652},
year = {2020}
}