Numerical homogenization of elliptic PDEs with similar coefficients
Numerical Analysis
2018-06-05 v2
Abstract
We consider a sequence of elliptic partial differential equations (PDEs) with different but similar rapidly varying coefficients. Such sequences appear, for example, in splitting schemes for time-dependent problems (with one coefficient per time step) and in sample based stochastic integration of outputs from an elliptic PDE (with one coefficient per sample member). We propose a parallelizable algorithm based on Petrov-Galerkin localized orthogonal decomposition (PG-LOD) that adaptively (using computable and theoretically derived error indicators) recomputes the local corrector problems only where it improves accuracy. The method is illustrated in detail by an example of a time-dependent two-pase Darcy flow problem in three dimensions.
Keywords
Cite
@article{arxiv.1703.08857,
title = {Numerical homogenization of elliptic PDEs with similar coefficients},
author = {Fredrik Hellman and Axel Målqvist},
journal= {arXiv preprint arXiv:1703.08857},
year = {2018}
}