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Original article (peer-reviewed)

Journal Journal of Scientific Computing
Volume (Issue) 78(2)
Page(s) 1272 - 1290
Title of proceedings Journal of Scientific Computing
DOI 10.1007/s10915-018-0807-6

Open Access

URL https://arxiv.org/abs/1801.10532
Type of Open Access Repository (Green Open Access)

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.
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