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Session I.1 - Multiresolution and Adaptivity in Numerical PDEs

Wednesday, June 14, 14:30 ~ 15:00

Multiresolution Super-Localized Orthogonal Decomposition

Daniel Peterseim

University of Augsburg, Germany   -   This email address is being protected from spambots. You need JavaScript enabled to view it.

We introduce a novel multiresolution super-localized orthogonal decomposition (SLOD) for the approximation of elliptic partial differential operators with arbitrarily rough coefficients. The method merges the concepts of (S)LOD and operator-adapted wavelets (gamblets). It computes hierarchical bases that block-diagonalize the partial differential operator and thereby decouple the discretization scales. At the same time, sparsity is enforced by a novel localization strategy that leads to a super-exponential decay of the basis functions relative to their discretization scales within the hierarchy.

Joint work with José C. Garay (University of Augsburg, Germany) and Christoph Zimmer (University of Augsburg, Germany).

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