Approximation Of Free Discontinuity Problems

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Approximation Of Free Discontinuity Problems

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Author : Andrea Braides
language : en
Publisher: Springer
Release Date : 2006-11-13

Approximation Of Free Discontinuity Problems written by Andrea Braides and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2006-11-13 with Mathematics categories.

Functionals involving both volume and surface energies have a number of applications ranging from Computer Vision to Fracture Mechanics. In order to tackle numerical and dynamical problems linked to such functionals many approximations by functionals defined on smooth functions have been proposed (using high-order singular perturbations, finite-difference or non-local energies, etc.) The purpose of this book is to present a global approach to these approximations using the theory of gamma-convergence and of special functions of bounded variation. The book is directed to PhD students and researchers in calculus of variations, interested in approximation problems with possible applications.

On The Approximation Of Free Discontinuity Problems

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Author : Luigi Ambrosio
language : en
Publisher:
Release Date : 1990

On The Approximation Of Free Discontinuity Problems written by Luigi Ambrosio and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1990 with categories.

Variational And Free Boundary Problems

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Author : Avner Friedman
language : en
Publisher: Springer Science & Business Media
Release Date : 2012-12-06

Variational And Free Boundary Problems written by Avner Friedman and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2012-12-06 with Science categories.

This IMA Volume in Mathematics and its Applications VARIATIONAL AND FREE BOUNDARY PROBLEMS is based on the proceedings of a workshop which was an integral part of the 1990- 91 IMA program on "Phase Transitions and Free Boundaries. " The aim of the workshop was to highlight new methods, directions and problems in variational and free boundary theory, with a concentration on novel applications of variational methods to applied problems. We thank R. Fosdick, M. E. Gurtin, W. -M. Ni and L. A. Peletier for organizing the year-long program and, especially, J. Sprock for co-organizing the meeting and co-editing these proceedings. We also take this opportunity to thank the National Science Foundation whose financial support made the workshop possible. Avner Friedman Willard Miller, Jr. PREFACE In a free boundary one seeks to find a solution u to a partial differential equation in a domain, a part r of its boundary of which is unknown. Thus both u and r must be determined. In addition to the standard boundary conditions on the un known domain, an additional condition must be prescribed on the free boundary. A classical example is the Stefan problem of melting of ice; here the temperature sat isfies the heat equation in the water region, and yet this region itself (or rather the ice-water interface) is unknown and must be determined together with the tempera ture within the water. Some free boundary problems lend themselves to variational formulation.

The Variational Approach To Fracture

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Author : Blaise Bourdin
language : en
Publisher: Springer Science & Business Media
Release Date : 2008-04-19

The Variational Approach To Fracture written by Blaise Bourdin and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2008-04-19 with Technology & Engineering categories.

Presenting original results from both theoretical and numerical viewpoints, this text offers a detailed discussion of the variational approach to brittle fracture. This approach views crack growth as the result of a competition between bulk and surface energy, treating crack evolution from its initiation all the way to the failure of a sample. The authors model crack initiation, crack path, and crack extension for arbitrary geometries and loads.

Iutam Symposium On Discretization Methods For Evolving Discontinuities

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Author : Alain Combescure
language : en
Publisher: Springer Science & Business Media
Release Date : 2010-04-07

Iutam Symposium On Discretization Methods For Evolving Discontinuities written by Alain Combescure and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2010-04-07 with Technology & Engineering categories.

In recent years, discretization methods have been proposed which are more flexible and which have the potential of capturing (moving) discontinuities in a robust and efficient manner. This monograph assembles contributions of leading experts with the most recent developments in this rapidly evolving field. It provides the most comprehensive coverage of state-of-the art numerical methods for treating discontinuities in mechanics.

Numerical Methods For Nonlinear Partial Differential Equations

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Author : Sören Bartels
language : en
Publisher: Springer
Release Date : 2015-01-19

Numerical Methods For Nonlinear Partial Differential Equations written by Sören Bartels and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2015-01-19 with Mathematics categories.

The description of many interesting phenomena in science and engineering leads to infinite-dimensional minimization or evolution problems that define nonlinear partial differential equations. While the development and analysis of numerical methods for linear partial differential equations is nearly complete, only few results are available in the case of nonlinear equations. This monograph devises numerical methods for nonlinear model problems arising in the mathematical description of phase transitions, large bending problems, image processing, and inelastic material behavior. For each of these problems the underlying mathematical model is discussed, the essential analytical properties are explained, and the proposed numerical method is rigorously analyzed. The practicality of the algorithms is illustrated by means of short implementations.

Calculus Of Variations And Partial Differential Equations

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Author : Luigi Ambrosio
language : en
Publisher: Springer Science & Business Media
Release Date : 2012-12-06

Calculus Of Variations And Partial Differential Equations written by Luigi Ambrosio and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2012-12-06 with Mathematics categories.

At the summer school in Pisa in September 1996, Luigi Ambrosio and Norman Dancer each gave a course on the geometric problem of evolution of a surface by mean curvature, and degree theory with applications to PDEs respectively. This self-contained presentation accessible to PhD students bridged the gap between standard courses and advanced research on these topics. The resulting book is divided accordingly into 2 parts, and neatly illustrates the 2-way interaction of problems and methods. Each of the courses is augmented and complemented by additional short chapters by other authors describing current research problems and results.

Foundations Of Computational Mathematics

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Author : Felipe Cucker
language : en
Publisher: Springer Science & Business Media
Release Date : 2012-12-06

Foundations Of Computational Mathematics written by Felipe Cucker and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2012-12-06 with Mathematics categories.

This book contains a collection of articles corresponding to some of the talks delivered at the Foundations of Computational Mathematics conference held at IMPA in Rio de Janeiro in January 1997. Some ofthe others are published in the December 1996 issue of the Journal of Complexity. Both of these publications were available and distributed at the meeting. Even in this aspect we hope to have achieved a synthesis of the mathematics and computer science cultures as well as of the disciplines. The reaction to the Park City meeting on Mathematics of Numerical Analy sis: Real Number Algorithms which was chaired by Steve Smale and had around 275 participants, was very enthusiastic. At the suggestion of Narendra Karmar mar a lunch time meeting of Felipe Cucker, Arieh Iserles, Narendra Karmarkar, Jim Renegar, Mike Shub and Steve Smale decided to try to hold a periodic meeting entitled "Foundations of Computational Mathematics" and to form an organization with the same name whose primary purpose will be to hold the meeting. This is then the first edition of FoCM as such. It has been organized around a small collection of workshops, namely - Systems of algebraic equations and computational algebraic geometry - Homotopy methods and real machines - Information-based complexity - Numerical linear algebra - Approximation and PDEs - Optimization - Differential equations and dynamical systems - Relations to computer science - Vision and related computational tools There were also twelve plenary speakers.

Gamma Convergence For Beginners

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Author : Andrea Braides
language : en
Publisher: Clarendon Press
Release Date : 2002-07-25

Gamma Convergence For Beginners written by Andrea Braides and has been published by Clarendon Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2002-07-25 with Mathematics categories.

The theory of Gamma-convergence is commonly recognized as an ideal and flexible tool for the description of the asymptotic behaviour of variational problems. Its applications range from the mathematical analysis of composites to the theory of phase transitions, from Image Processing to Fracture Mechanics. This text, written by an expert in the field, provides a brief and simple introduction to this subject, based on the treatment of a series of fundamental problems that illustrate the main features and techniques of Gamma-convergence and at the same time provide a stimulating starting point for further studies. The main part is set in a one-dimensional framework that highlights the main issues of Gamma-convergence without the burden of higher-dimensional technicalities. The text deals in sequence with increasingly complex problems, first treating integral functionals, then homogenisation, segmentation problems, phase transitions, free-discontinuity problems and their discrete and continuous approximation, making stimulating connections among those problems and with applications. The final part is devoted to an introduction to higher-dimensional problems, where more technical tools are usually needed, but the main techniques of Gamma-convergence illustrated in the previous section may be applied unchanged. The book and its structure originate from the author's experience in teaching courses on this subject to students at PhD level in all fields of Applied Analysis, and from the interaction with many specialists in Mechanics and Computer Vision, which have helped in making the text addressed also to a non-mathematical audience. The material of the book is almost self-contained, requiring only some basic notion of Measure Theory and Functional Analysis.

Theoretical Foundations And Numerical Methods For Sparse Recovery

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Author : Massimo Fornasier
language : en
Publisher: Walter de Gruyter
Release Date : 2010-07-30

Theoretical Foundations And Numerical Methods For Sparse Recovery written by Massimo Fornasier and has been published by Walter de Gruyter this book supported file pdf, txt, epub, kindle and other format this book has been release on 2010-07-30 with Mathematics categories.

The present collection is the very first contribution of this type in the field of sparse recovery. Compressed sensing is one of the important facets of the broader concept presented in the book, which by now has made connections with other branches such as mathematical imaging, inverse problems, numerical analysis and simulation. The book consists of four lecture notes of courses given at the Summer School on "Theoretical Foundations and Numerical Methods for Sparse Recovery" held at the Johann Radon Institute for Computational and Applied Mathematics in Linz, Austria, in September 2009. This unique collection will be of value for a broad community and may serve as a textbook for graduate courses. From the contents: "Compressive Sensing and Structured Random Matrices" by Holger Rauhut "Numerical Methods for Sparse Recovery" by Massimo Fornasier "Sparse Recovery in Inverse Problems" by Ronny Ramlau and Gerd Teschke "An Introduction to Total Variation for Image Analysis" by Antonin Chambolle, Vicent Caselles, Daniel Cremers, Matteo Novaga and Thomas Pock