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Title

Algebraic Tools and Multiscale Methods for the Numerical Integration of Stochastic Evolutionary Problems

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Director
Defense Thèse de doctorat : Univ. Genève, 2021 - Sc. 5570 - 2021/07/02
Abstract The aim of the work presented in this thesis is the construction and the study of numerical integrators in time to solve stochastic differential equations (SDEs) and stochastic partial differential equations (SPDEs). More precisely, we are interested in the convergence of the methods, in the weak sense and for sampling the invariant measure in the case of ergodic dynamics, introducing a new algebraic framework of trees for the computation of order conditions. We focus on the preservation of geometric properties by the numerical integrators, in particular invariants and constraints, as well as on the robustness of the methods in the case of multiscale problems.
Keywords Stochastic differential equationsGeometric numerical integrationOverdamped Langevin dynamicInvariant measureErgodicityExotic aromatic Butcher-seriesAlgebraicOrder conditionManifoldsNonlinear Schrödinger equationWhite noise dispersionHighly-oscillatory SDEsMultirevolution methods
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URN: urn:nbn:ch:unige-1537965
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Thesis (4 MB) - public document Free access
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Research group Analyse numérique
Projects
FNS: 200020_184614
FNS: 200021_162404
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LAURENT, Adrien. Algebraic Tools and Multiscale Methods for the Numerical Integration of Stochastic Evolutionary Problems. Université de Genève. Thèse, 2021. doi: 10.13097/archive-ouverte/unige:153796 https://archive-ouverte.unige.ch/unige:153796

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Deposited on : 2021-08-09

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