Repository: Freie Universit├Ąt Berlin, Math Department

NUMERICAL HOMOGENIZATION OF FRACTAL INTERFACE PROBLEMS

KORNHUBER, RALF and PODLESNY, JOSCHA and YSERENTANT, HARRY (2020) NUMERICAL HOMOGENIZATION OF FRACTAL INTERFACE PROBLEMS. arXive . pp. 1-30. (Submitted)

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Official URL: https://arxiv.org/abs/2007.11479

Abstract

We consider the numerical homogenization of a class of fractal elliptic interface problems inspired by related mechanical contact problems from the geosciences. A particular feature is that the solution space depends on the actual fractal geometry. Our main results concern the construction of projection operators with suitable stability and approximation properties. The existence of such projections then allows for the application of existing concepts from localized orthogonal decomposition (LOD) and successive subspace correction to construct first multiscale discretizations and iterative algebraic solvers with scale-independent convergence behavior for this class of problems.

Item Type:Article
Subjects:Mathematical and Computer Sciences > Mathematics > Applied Mathematics
Divisions:Department of Mathematics and Computer Science > Institute of Mathematics
ID Code:2486
Deposited By: Monika Drueck
Deposited On:16 Feb 2021 14:16
Last Modified:17 Feb 2021 06:41

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