Computational and Applied Mathematics (CAM) seminar

​​Moritz Hauck, University of Augsburg: Super-localization of elliptic multi-scale problems with an extension to spatial networks
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Abstract: Numerical homogenization aims to efficiently and accurately approximate the solution space of an elliptic partial differential operator with arbitrarily rough (non-periodic) coefficients. The application of the inverse operator to some standard finite element space defines an approximation space with uniform algebraic approximation rates with respect to the mesh size. This holds even for under-resolved rough coefficients. However, the canonical basis associated with this construction is non-local and, hence, numerically infeasible. This is why the true challenge of numerical homogenization is the identification of a computable local basis for such an operator-dependent approximate solution space. This talk introduces a constructive and near optimal solution to this localization problem for the prototypical elliptic model problem along with possible generalizations. In particular, the construction carries over to the setting of a weighted graph Laplacian on spatial networks fulfilling certain connectivity and homogeneity assumptions which enables near optimal localization also for such problems. A sequence of numerical experiments illustrates the significance of the novel localization technique when compared to other state-of-the-art results.
​​Organiser: David Cohen (david.cohen@chalmers.se). Please contact me if you need the Zoom password. Zoom meeting link: https://chalmers.zoom.us/j/69309989575
Category Seminar
Location: MV:L14, Chalmers tvärgata 3
Starts: 28 September, 2022, 13:15
Ends: 28 September, 2022, 14:00

Page manager Published: Tue 27 Sep 2022.