Analyse de méthodes de résolution parallèles d’EDO/EDA raides

Abstract : This PhD Thesis deals with the development of parallel numerical methods for solving Ordinary and Algebraic Differential Equations. ODE and DAE are commonly arising when modeling complex dynamical phenomena. We first show that the parallelization across the method is limited by the number of stages of the RK method or DIMSIM. We introduce the Schur complement into the linearised linear system of time integrators. An automatic framework is given to build a mask defining the relationships between the variables. Then the Schur complement is coupled with Jacobian Free Newton-Krylov methods. As time decomposition, global time steps resolutions can be solved by parallel nonlinear solvers (such as fixed point, Newton and Steffensen acceleration). Two steps time decomposition (Parareal, Pita,...) are developed with a new definition of their grids to solved stiff problems. Global error estimates, especially the Richardson extrapolation, are used to compute a good approximation for the second grid. Finally we propose a parallel deferred correction
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David Guibert. Analyse de méthodes de résolution parallèles d’EDO/EDA raides. Mathématiques générales [math.GM]. Université Claude Bernard - Lyon I, 2009. Français. ⟨NNT : 2009LYO10138⟩. ⟨tel-00430013v2⟩

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