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Author : Ralf Kornhuber
Release : 1997
Genre : Mathematics
Kind : eBook
Book Rating : /5 ( reviews)
Book Synopsis Adaptive Monotone Multigrid Methods for Nonlinear Variational Problems by : Ralf Kornhuber
Download or read book Adaptive Monotone Multigrid Methods for Nonlinear Variational Problems written by Ralf Kornhuber. This book was released on 1997. Available in PDF, EPUB and Kindle. Book excerpt:
Author : Ralf Kornhuber
Release : 1996
Genre : Boundary value problems
Kind : eBook
Book Rating : /5 ( reviews)
Book Synopsis On Robust Multigrid Methods for Non-smooth Variational Problems by : Ralf Kornhuber
Download or read book On Robust Multigrid Methods for Non-smooth Variational Problems written by Ralf Kornhuber. This book was released on 1996. Available in PDF, EPUB and Kindle. Book excerpt: 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."
Author : Michael Ulbrich
Release : 2011-01-01
Genre : Constrained optimization
Kind : eBook
Book Rating : 692/5 ( reviews)
Book Synopsis Semismooth Newton Methods for Variational Inequalities and Constrained Optimization Problems in Function Spaces by : Michael Ulbrich
Download or read book Semismooth Newton Methods for Variational Inequalities and Constrained Optimization Problems in Function Spaces written by Michael Ulbrich. This book was released on 2011-01-01. Available in PDF, EPUB and Kindle. Book excerpt: Semismooth Newton methods are a modern class of remarkably powerful and versatile algorithms for solving constrained optimization problems with partial differential equations (PDEs), variational inequalities, and related problems. This book provides a comprehensive presentation of these methods in function spaces, striking a balance between thoroughly developed theory and numerical applications. Although largely self-contained, the book also covers recent developments in the field, such as state-constrained problems, and offers new material on topics such as improved mesh independence results. The theory and methods are applied to a range of practically important problems, including: optimal control of nonlinear elliptic differential equations, obstacle problems, and flow control of instationary Navier-Stokes fluids. In addition, the author covers adjoint-based derivative computation and the efficient solution of Newton systems by multigrid and preconditioned iterative methods.
Author : James Blowey
Release : 2013-03-09
Genre : Mathematics
Kind : eBook
Book Rating : 548/5 ( reviews)
Book Synopsis Theory and Numerics of Differential Equations by : James Blowey
Download or read book Theory and Numerics of Differential Equations written by James Blowey. This book was released on 2013-03-09. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Author : Gianni Pillo
Release : 2006-06-03
Genre : Mathematics
Kind : eBook
Book Rating : 651/5 ( reviews)
Book Synopsis Large-Scale Nonlinear Optimization by : Gianni Pillo
Download or read book Large-Scale Nonlinear Optimization written by Gianni Pillo. This book was released on 2006-06-03. Available in PDF, EPUB and Kindle. Book excerpt: This book reviews and discusses recent advances in the development of methods and algorithms for nonlinear optimization and its applications, focusing on the large-dimensional case, the current forefront of much research. Individual chapters, contributed by eminent authorities, provide an up-to-date overview of the field from different and complementary standpoints, including theoretical analysis, algorithmic development, implementation issues and applications.
