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

Harbrecht, Helmut and Zaspel, Peter. (2019) On the algebraic construction of sparse multilevel approximations of elliptic tensor product problems. Journal of scientific computing, 78 (2). pp. 1272-1290.

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Abstract

We consider the solution of elliptic problems on the tensor product of two physical domains as for example 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. 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)
UniBasel Contributors:Harbrecht, Helmut and Zaspel, Peter
Item Type:Article, refereed
Article Subtype:Research Article
Publisher:Springer
ISSN:0885-7474
e-ISSN:1573-7691
Note:Publication type according to Uni Basel Research Database: Journal article
Language:English
Identification Number:
Last Modified:19 Mar 2019 14:23
Deposited On:19 Mar 2019 14:23

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