| Zugriffsnummer | 51144 |
| Dokumenttyp | Zeitschriftenartikel |
| Peer Review | mit Peer Review |
| Sprache | Englisch |
| Titel | Adaptive nonintrusive reconstruction of solutions to high-dimensional parametric PDEs |
| Autor(in); Institution |
Eigel, Martin; Weierstrass Institute for Applied Analysis and Stochastics Berlin, GERMANY
Trunschke, Philipp; Technische Universität Berlin, Berlin, GERMANY
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| Quelle/Jahr | SIAM Journal on Scientific Computing: 45 (2023), 2, A457 - A479 |
| Artikelnummer | 1137 |
| ISSN | 1064-8275 (online) |
| DOI | |
| Persistent Identifier | |
| URL | |
| Verlag | siam |
| Freie Schlagworte | uncertainty quantification ; adaptive ; low-rank tensor regression ; tensor train ; parametric PDEs ; residual error estimator ; stochastic Galerkin finite element method |
| Zusammenfassung | Numerical methods for random parametric PDEs can greatly benefit from adaptive refinement schemes, in particular when functional approximations are computed as in stochastic Galerkin and stochastic collocations methods. This work is concerned with a nonintrusive generalization of the adaptive Galerkin finite element method with residual-based error estimation. It combines the nonintrusive character of a randomized least squares method with the a posteriori error analysis of stochastic Galerkin methods. The proposed approach uses the variational Monte Carlo method to obtain a quasi-optimal low-rank approximation of the Galerkin projection in a highly efficient hierarchical tensor format. We derive an adaptive refinement algorithm which is steered by a reliable error estimator. Opposite to stochastic Galerkin methods, the approach is easily applicable to a wide range of problems, enabling a fully automated adjustment of all discretization parameters. Benchmark examples with affine and (unbounded) lognormal coefficient fields illustrate the performance of the nonintrusive adaptive algorithm, showing the expected convergence rates of single-level strategies. Auch unter Arxiv erschienen: https://arxiv.org/pdf/2112.01285.pdf |
| Themenbereich der Metrologie | Metrologie in der Medizin |