Stefan Takacs

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For iterative solvers, besides convergence proofs that may state qualitative results for some classes of problems, straightforward methods to compute (bounds for) convergence rates are of particular interest. A widely-used straightforward method to analyze the convergence of numerical methods for solving discretized systems of partial differential equations(More)
—Local Fourier analysis is a strong and well-established tool for analyzing the convergence of numerical methods for partial differential equations. The key idea of local Fourier analysis is to represent the occurring functions in terms of a Fourier series and to use this representation to study certain properties of the particular numerical method, like(More)
In the present paper we concentrate on an important issue in constructing a good multigrid solver: the choice of an efficient smoother. We will introduce all-at-once multigrid solvers for optimal control problems which show robust convergence in the grid size and in the regular-ization parameter. We will refer to recent publications that guarantee such a(More)
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