Name
Abstract | ||
|---|---|---|
We propose a novel combination of the reduced basis method with low-rank tensor techniques for the efficient solution of parameter-dependent linear systems in the case of several parameters. This combination, called rbTensor, consists of three ingredients. First, the underlying parameter-dependent operator is approximated by an explicit affine representation in a low-rank tensor format. Second, a standard greedy strategy is used to construct a problem-dependent reduced basis. Third, the associated reduced parametric system is solved for all parameter values on a tensor grid simultaneously via a low-rank approach. This allows us to explicitly represent and store an approximate solution for all parameter values at a time. Once this approximation is available, the computation of output functionals and the evaluation of statistics of the solution become a cheap online task, without requiring the solution of a linear system. |
Year | DOI | Venue |
|---|---|---|
2016 | 10.1137/15M1042784 | SIAM JOURNAL ON SCIENTIFIC COMPUTING |
Keywords | Field | DocType |
reduced basis method,parametric partial differential equation,hierarchical tensor format,low-rank tensor | Tensor product,Tensor density,Mathematical optimization,Tensor (intrinsic definition),Tensor,Mathematical analysis,Cartesian tensor,Symmetric tensor,Tensor product of Hilbert spaces,Tensor contraction,Mathematics | Journal |
Volume | Issue | ISSN |
38 | 4 | 1064-8275 |
Citations | PageRank | References |
0 | 0.34 | 17 |
Authors | ||
2 | ||
Name | Order | Citations | PageRank |
|---|---|---|---|
| Jonas Ballani | 1 | 0 | 0.34 |
| Daniel Kressner | 2 | 449 | 48.01 |