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On the algebraic construction of sparse multilevel approximations of elliptic tensor product problems

Harbrecht, Helmut and Zaspel, Peter Eberhard. (2018) On the algebraic construction of sparse multilevel approximations of elliptic tensor product problems. Preprints Fachbereich Mathematik, 2018 (01).

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Official URL: https://edoc.unibas.ch/69928/

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Abstract

We consider the solution of elliptic problems on the tensor product of two physical domains as e.g. present in the approximation of the solution covariance of elliptic partial differential equations with random input. Previous sparse approximation approaches used a geometrically constructed multilevel hierarchy. Instead, we construct this hierarchy for a given discretized problem by means of the algebraic multigrid method (AMG). Thereby, we are able to apply the sparse grid combination technique to problems given on complex geometries and for discretizations arising from unstructured grids, which was not feasible before. Numerical results show that our algebraic construction exhibits the same convergence behaviour as the geometric construction, while being applicable even in black-box type PDE solvers.
Faculties and Departments:05 Faculty of Science > Departement Mathematik und Informatik > Mathematik > Computational Mathematics (Harbrecht)
12 Special Collections > Preprints Fachbereich Mathematik
UniBasel Contributors:Harbrecht, Helmut and Zaspel, Peter
Item Type:Preprint
Publisher:Universität Basel
Language:English
Last Modified:17 Apr 2019 19:53
Deposited On:28 Mar 2019 09:51

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