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arXiv · 1703.08857

Numerical homogenization of elliptic PDEs with similar coefficients

Fredrik Hellman·Axel Målqvist
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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.

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Fredrik Hellman, Axel Målqvist. 2017-03-26. Numerical homogenization of elliptic PDEs with similar coefficients. https://arxiv.org/abs/1703.08857

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