Stochastic methods for solving high-dimensional partial differential equations
| Autor: | Anthony Nouy, Arthur Macherey, Marie Billaud-Friess, Clémentine Prieur |
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| Přispěvatelé: | Laboratoire de Mathématiques Jean Leray (LMJL), Centre National de la Recherche Scientifique (CNRS)-Université de Nantes - UFR des Sciences et des Techniques (UN UFR ST), Université de Nantes (UN)-Université de Nantes (UN), École Centrale de Nantes (ECN), Méthodes d'Analyse Stochastique des Codes et Traitements Numériques (GdR MASCOT-NUM), Centre National de la Recherche Scientifique (CNRS), Mathematics and computing applied to oceanic and atmospheric flows (AIRSEA), Inria Grenoble - Rhône-Alpes, Institut National de Recherche en Informatique et en Automatique (Inria)-Institut National de Recherche en Informatique et en Automatique (Inria)-Université Grenoble Alpes (UGA)-Laboratoire Jean Kuntzmann (LJK), Institut National de Recherche en Informatique et en Automatique (Inria)-Centre National de la Recherche Scientifique (CNRS)-Université Grenoble Alpes (UGA)-Institut polytechnique de Grenoble - Grenoble Institute of Technology (Grenoble INP ), Université Grenoble Alpes (UGA)-Centre National de la Recherche Scientifique (CNRS)-Institut polytechnique de Grenoble - Grenoble Institute of Technology (Grenoble INP ), Université Grenoble Alpes (UGA), Université de Nantes - UFR des Sciences et des Techniques (UN UFR ST), Université de Nantes (UN)-Université de Nantes (UN)-Centre National de la Recherche Scientifique (CNRS), ANR-11-LABX-0020,LEBESGUE,Centre de Mathématiques Henri Lebesgue : fondements, interactions, applications et Formation(2011) |
| Jazyk: | angličtina |
| Rok vydání: | 2018 |
| Předmět: |
Pointwise
Partial differential equation Computer science Probabilistic logic MathematicsofComputing_NUMERICALANALYSIS Numerical Analysis (math.NA) 010103 numerical & computational mathematics High dimensional 16. Peace & justice Control variates 01 natural sciences Interpretation (model theory) 010104 statistics & probability ComputingMethodologies_SYMBOLICANDALGEBRAICMANIPULATION FOS: Mathematics Applied mathematics Shaping Mathematics - Numerical Analysis 0101 mathematics Representation (mathematics) [MATH.MATH-NA]Mathematics [math]/Numerical Analysis [math.NA] |
| Zdroj: | Springer Proceedings in Mathematics & Statistics International Conference on Monte Carlo and Quasi-Monte Carlo Methods in Scientific Computing-MCQMC 2018 International Conference on Monte Carlo and Quasi-Monte Carlo Methods in Scientific Computing-MCQMC 2018, Jul 2018, Rennes, France. pp.125-141, ⟨10.1007/978-3-030-43465-6_6⟩ Springer Proceedings in Mathematics & Statistics ISBN: 9783030434649 |
| ISSN: | 2194-1009 |
| DOI: | 10.1007/978-3-030-43465-6_6⟩ |
| Popis: | International audience; We propose algorithms for solving high-dimensional Partial Differential Equations (PDEs) that combine a probabilistic interpretation of PDEs, through Feynman-Kac representation, with sparse interpolation. Monte-Carlo methods and time-integration schemes are used to estimate pointwise evaluations of the solution of a PDE. We use a sequential control variates algorithm, where control variates are constructed based on successive approximations of the solution of the PDE. Two different algorithms are proposed, combining in different ways the sequential control variates algorithm and adaptive sparse interpolation. Numerical examples will illustrate the behavior of these algorithms. |
| Databáze: | OpenAIRE |
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