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Alocal Fourierconvergenceanalysisof …

A local Fourier convergence analysis of a multigrid method using symbolic computation Veronika Pillwein Stefan Takacs DK-Report No. 2012-04 04 2012. A 4040 LINZ, ALTENBERGERSTRASSE 69, AUSTRIA. Supported by Austrian Science Fund (FWF) Upper Austria Editorial Board: Bruno Buchberger Bert J uttler Ulrich Langer Manuel Kauers Esther Klann Peter Paule Clemens Pechstein Veronika Pillwein Ronny Ramlau Josef Schicho Wolfgang Schreiner Franz Winkler Walter Zulehner Managing Editor: Veronika Pillwein Communicated by: Manuel Kauers Walter Zulehner DK sponsors: Johannes Kepler University Linz (JKU). Austrian Science Fund (FWF). Upper Austria A LOCAL FOURIER CONVERGENCE ANALYSIS OF A. MULTIGRID METHOD USING SYMBOLIC COMPUTATION. VERONIKA PILLWEIN AND STEFAN TAKACS. Abstract. For iterative solvers, besides convergence proofs that may state qualitative results for some classes of problems, straight-forward methods to compute (bounds for) convergence rates are of particular interest. A widely- used straight-forward method to analyze the convergence of numerical methods for solving discretized systems of partial differential equations (PDEs) is local Fourier analysis (or local mode analysis).

2 VERONIKA PILLWEIN AND STEFAN TAKACS As a model problem for the proposed machinery, we choose the application of a multigrid method to a particular PDE-constrained optimization problem.

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  Optimization, Constrained, Constrained optimization

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