MATHICSE Technical Report : Multi-index stochastic collocation for random PDEs
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| Titel: | MATHICSE Technical Report : Multi-index stochastic collocation for random PDEs |
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| Autoren: | Haji Ali, Abdul Lateef, Nobile, Fabio, Tamellini, Lorenzo, Tempone, Raùl |
| Weitere Verfasser: | MATHICSE-Group |
| Verlagsinformationen: | MATHICSE Écublens |
| Publikationsjahr: | 2019 |
| Bestand: | Ecole Polytechnique Fédérale Lausanne (EPFL): Infoscience |
| Schlagwörter: | Uncertainty Quantiffication, Random PDEs, Multivariate approximation, Sparse grids, Stochastic Collocation methods, Multilevel methods, Combination technique |
| Beschreibung: | In this work we introduce the Multi-Index Stochastic Collocation method (MISC) for computing statistics of the solution of a PDE with random data. MISC is a combination technique based on mixed differences of spatial approximations and quadratures over the space of random data. We propose an optimization procedure to select the most eective mixed differences to include in the MISC estimator: such optimization is a crucial step and allows us to build a method that, provided with sufficient solution regularity, is potentially more eective than other multi-level collocation methods already available in literature. We then provide a complexity analysis that assumes decay rates of product type for such mixed differences, showing that in the optimal case the convergence rate of MISC is only dictated by the convergence of the deterministic solver applied to a one dimensional problem. We show the effectiveness of MISC with some computational tests, comparing it with other related methods available in the literature, such as the Multi- Index and Multilevel Monte Carlo, Multilevel Stochastic Collocation, Quasi Optimal Stochastic Collocation and Sparse Composite Collocation methods. ; CSQI ; MATHICSE Technical Report Nr. 22.2015 September 2015 |
| Publikationsart: | report |
| Sprache: | unknown |
| Relation: | https://infoscience.epfl.ch/record/263551/files/22.2015_AH-FN-LT-RT.pdf; #PLACEHOLDER_PARENT_METADATA_VALUE#; https://infoscience.epfl.ch/handle/20.500.14299/154076 |
| DOI: | 10.5075/epfl-MATHICSE-263551 |
| Verfügbarkeit: | https://doi.org/10.5075/epfl-MATHICSE-263551 https://infoscience.epfl.ch/handle/20.500.14299/154076 https://hdl.handle.net/20.500.14299/154076 |
| Dokumentencode: | edsbas.3BAC183D |
| Datenbank: | BASE |
Nájsť tento článok vo Web of Science | Abstract: | In this work we introduce the Multi-Index Stochastic Collocation method (MISC) for computing statistics of the solution of a PDE with random data. MISC is a combination technique based on mixed differences of spatial approximations and quadratures over the space of random data. We propose an optimization procedure to select the most eective mixed differences to include in the MISC estimator: such optimization is a crucial step and allows us to build a method that, provided with sufficient solution regularity, is potentially more eective than other multi-level collocation methods already available in literature. We then provide a complexity analysis that assumes decay rates of product type for such mixed differences, showing that in the optimal case the convergence rate of MISC is only dictated by the convergence of the deterministic solver applied to a one dimensional problem. We show the effectiveness of MISC with some computational tests, comparing it with other related methods available in the literature, such as the Multi- Index and Multilevel Monte Carlo, Multilevel Stochastic Collocation, Quasi Optimal Stochastic Collocation and Sparse Composite Collocation methods. ; CSQI ; MATHICSE Technical Report Nr. 22.2015 September 2015 |
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| DOI: | 10.5075/epfl-MATHICSE-263551 |