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Convergence analysis of substructuring Waveform Relaxation methods for space-time problems and their application to Optimal Control Problems

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Defense Thèse de doctorat : Univ. Genève, 2014 - Sc. 4745 - 2014/12/15
Abstract This thesis contributes to develop a new class of methods for the numerical solution of partial differential equations (PDEs) using space-time domain decomposition algorithms to ensure the use of different time steps in different subdomains. We first introduce and analyze new types of Waveform Relaxation methods based on the Dirichlet-Neumann and Neumann-Neumann methods, for parabolic and hyperbolic problems. The algorithms, formally termed as Dirichlet-Neumann Waveform Relaxation (DNWR) and Neumann-Neumann Waveform Relaxation (NNWR), generalize the use of substructuring methods to the case of evolution problems in a natural way. We finally propose an application of these methods for PDE-constrained Optimal Control Problems, solving the underlying forward and adjoint PDEs using a domain decomposition method. We apply and analyze the Dirichlet-Neumann and Neumann-Neumann methods on control problems and give the optimal choice of relaxation parameters for both the forward and adjoint problems in the steady as well as time-dependent case.
Keywords Space-time domain decompositionWaveform RelaxationDirichlet-Neumann Waveform RelaxationNeumann-Neumann Waveform RelaxationOptimized Schwarz Waveform RelaxationOptimal Control Problems
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URN: urn:nbn:ch:unige-461468
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Thesis (5.2 MB) - public document Free access
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Research group Analyse numérique
Projects FNS: 200020_149107/1
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MANDAL, Bankim. Convergence analysis of substructuring Waveform Relaxation methods for space-time problems and their application to Optimal Control Problems. Université de Genève. Thèse, 2014. https://archive-ouverte.unige.ch/unige:46146

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Deposited on : 2015-02-02

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