On Robust Multigrid Methods for Non-smooth Variational Problems - read free eBook in online reader or directly download on the web page. Select files or add your book in reader. Download and read online ebook On Robust Multigrid Methods for Non-smooth Variational Problems write by Ralf Kornhuber. This book was released on 1996. On Robust Multigrid Methods for Non-smooth Variational Problems available in PDF, EPUB and Kindle. Abstract: "We consider the fast solution of large, piecewise smooth minimization problems as resulting from the approximation of elliptic free boundary problems. The most delicate question in constructing a multigrid method for a nonlinear, non-smooth problem is how to represent the nonlinearity on the coarse grids. This process usually involves some kind of linearization. The basic idea of monotone multigrid methods to be presented here is first to select a neighborhood of the actual smoothed iterate in which a linearization is possible and then to constrain the coarse grid correction to this neighborhood. Such a local linearization allows to control the local corrections at each coarse grid node in such a way that the energy functional is monotonically decreasing. This approach leads to globally convergent schemes which are robust with respect to local singularities of the given problem. The numerical performance is illustrated by approximating the well-known Barenblatt solution of the porous medium equation."
Adaptive Monotone Multigrid Methods for Nonlinear Variational Problems
Adaptive Monotone Multigrid Methods for Nonlinear Variational Problems - read free eBook in online reader or directly download on the web page. Select files or add your book in reader. Download and read online ebook Adaptive Monotone Multigrid Methods for Nonlinear Variational Problems write by Ralf Kornhuber. This book was released on 1997. Adaptive Monotone Multigrid Methods for Nonlinear Variational Problems available in PDF, EPUB and Kindle.
Multigrid Methods V
Multigrid Methods V - read free eBook in online reader or directly download on the web page. Select files or add your book in reader. Download and read online ebook Multigrid Methods V write by Wolfgang Hackbusch. This book was released on 2012-12-06. Multigrid Methods V available in PDF, EPUB and Kindle. This volume contains a selection from the papers presented at the Fifth European Multigrid Conference, held in Stuttgart, October 1996. All contributions were carefully refereed. The conference was organized by the Institute for Computer Applications (ICA) of the University of Stuttgart, in cooperation with the GAMM Committee for Scientific Computing, SFB 359 and 404 and the research network WiR Ba-Wü. The list of topics contained lectures on Multigrid Methods: robustness, adaptivity, wavelets, parallelization, application in computational fluid dynamics, porous media flow, optimisation and computational mechanics. A considerable part of the talks focused on algebraic multigrid methods.
Towards Robust Algebraic Multigrid Methods for Nonsymmetric Problems
Towards Robust Algebraic Multigrid Methods for Nonsymmetric Problems - read free eBook in online reader or directly download on the web page. Select files or add your book in reader. Download and read online ebook Towards Robust Algebraic Multigrid Methods for Nonsymmetric Problems write by James Lottes. This book was released on 2017-03-24. Towards Robust Algebraic Multigrid Methods for Nonsymmetric Problems available in PDF, EPUB and Kindle. This thesis presents a rigorous, abstract analysis of multigrid methods for positive nonsymmetric problems, particularly suited to algebraic multigrid, with a completely new approach to nonsymmetry which is based on a new concept of absolute value for nonsymmetric operators. Multigrid, and in particular algebraic multigrid, has become an indispensable tool for the solution of discretizations of partial differential equations. While used in both the symmetric and nonsymmetric cases, the theory for the nonsymmetric case has lagged substantially behind that for the symmetric case. This thesis closes some of this gap, presenting a major and highly original contribution to an important problem of computational science. The new approach to nonsymmetry will be of interest to anyone working on the analysis of discretizations of nonsymmetric operators, even outside the context of multigrid. The presentation of the convergence theory may interest even those only concerned with the symmetric case, as it sheds some new light on and extends existing results.
Theory and Numerics of Differential Equations
Theory and Numerics of Differential Equations - read free eBook in online reader or directly download on the web page. Select files or add your book in reader. Download and read online ebook Theory and Numerics of Differential Equations write by James Blowey. This book was released on 2013-03-09. Theory and Numerics of Differential Equations available in PDF, EPUB and Kindle. A compilation of detailed lecture notes on six topics at the forefront of current research in numerical analysis and applied mathematics. Each set of notes presents a self-contained guide to a current research area and has an extensive bibliography. In addition, most of the notes contain detailed proofs of the key results. The notes start from a level suitable for first year graduate students in applied mathematics, mathematical analysis or numerical analysis, and proceed to current research topics. The reader should therefore be able to quickly gain an insight into the important results and techniques in each area without recourse to the large research literature. Current (unsolved) problems are also described and directions for future research is given.
