Sobolev Gradients And Differential Equations

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Sobolev Gradients And Differential Equations

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Author : john neuberger
language : en
Publisher: Springer
Release Date : 2009-11-10

Sobolev Gradients And Differential Equations written by john neuberger and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2009-11-10 with Mathematics categories.

A Sobolev gradient of a real-valued functional on a Hilbert space is a gradient of that functional taken relative to an underlying Sobolev norm. This book shows how descent methods using such gradients allow a unified treatment of a wide variety of problems in differential equations. For discrete versions of partial differential equations, corresponding Sobolev gradients are seen to be vastly more efficient than ordinary gradients. In fact, descent methods with these gradients generally scale linearly with the number of grid points, in sharp contrast with the use of ordinary gradients. Aside from the first edition of this work, this is the only known account of Sobolev gradients in book form. Most of the applications in this book have emerged since the first edition was published some twelve years ago. What remains of the first edition has been extensively revised. There are a number of plots of results from calculations and a sample MatLab code is included for a simple problem. Those working through a fair portion of the material have in the past been able to use the theory on their own applications and also gain an appreciation of the possibility of a rather comprehensive point of view on the subject of partial differential equations.

Sobolev Gradients And Differential Equations

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Author : john neuberger
language : en
Publisher: Springer
Release Date : 2006-11-13

Sobolev Gradients And Differential Equations written by john neuberger 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.

A Sobolev gradient of a real-valued functional is a gradient of that functional taken relative to the underlying Sobolev norm. This book shows how descent methods using such gradients allow a unified treatment of a wide variety of problems in differential equations. Equal emphasis is placed on numerical and theoretical matters. Several concrete applications are made to illustrate the method. These applications include (1) Ginzburg-Landau functionals of superconductivity, (2) problems of transonic flow in which type depends locally on nonlinearities, and (3) minimal surface problems. Sobolev gradient constructions rely on a study of orthogonal projections onto graphs of closed densely defined linear transformations from one Hilbert space to another. These developments use work of Weyl, von Neumann and Beurling.

Sobolev Gradients And Differential Equations

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Author : John Neuberger
language : en
Publisher: Springer Science & Business Media
Release Date : 2009-12-01

Sobolev Gradients And Differential Equations written by John Neuberger 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 2009-12-01 with Mathematics categories.

A Sobolev gradient of a real-valued functional on a Hilbert space is a gradient of that functional taken relative to an underlying Sobolev norm. This book shows how descent methods using such gradients allow a unified treatment of a wide variety of problems in differential equations. For discrete versions of partial differential equations, corresponding Sobolev gradients are seen to be vastly more efficient than ordinary gradients. In fact, descent methods with these gradients generally scale linearly with the number of grid points, in sharp contrast with the use of ordinary gradients. Aside from the first edition of this work, this is the only known account of Sobolev gradients in book form. Most of the applications in this book have emerged since the first edition was published some twelve years ago. What remains of the first edition has been extensively revised. There are a number of plots of results from calculations and a sample MatLab code is included for a simple problem. Those working through a fair portion of the material have in the past been able to use the theory on their own applications and also gain an appreciation of the possibility of a rather comprehensive point of view on the subject of partial differential equations.

Sobolev Gradients And Differential Equations

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Author : John William Neuberger
language : de
Publisher:
Release Date : 1997

Sobolev Gradients And Differential Equations written by John William Neuberger and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1997 with categories.

Sobolev Gradients And Differential Equations

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Author : John W. Neuberger
language : en
Publisher:
Release Date : 1997

Sobolev Gradients And Differential Equations written by John W. Neuberger and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1997 with Mathematics categories.

A Sobolev gradient of a real-valued functional is a gradient of that functional taken relative to the underlying Sobolev norm. This book shows how descent methods using such gradients allow a unified treatment of a wide variety of problems in differential equations. Equal emphasis is placed on numerical and theoretical matters. Several concrete applications are made to illustrate the method. These applications include (1) Ginzburg-Landau functionals of superconductivity, (2) problems of transonic flow in which type depends locally on nonlinearities, and (3) minimal surface problems. Sobolev gradient constructions rely on a study of orthogonal projections onto graphs of closed densely defined linear transformations from one Hilbert space to another. These developments use work of Weyl, von Neumann and Beurling.

Data Driven Models In Inverse Problems

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Author : Tatiana A. Bubba
language : en
Publisher: Walter de Gruyter GmbH & Co KG
Release Date : 2024-11-18

Data Driven Models In Inverse Problems written by Tatiana A. Bubba and has been published by Walter de Gruyter GmbH & Co KG this book supported file pdf, txt, epub, kindle and other format this book has been release on 2024-11-18 with Mathematics categories.

Advances in learning-based methods are revolutionizing several fields in applied mathematics, including inverse problems, resulting in a major paradigm shift towards data-driven approaches. This volume, which is inspired by this cutting-edge area of research, brings together contributors from the inverse problem community and shows how to successfully combine model- and data-driven approaches to gain insight into practical and theoretical issues.

Variational Methods Open Problems Recent Progress And Numerical Algorithms

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Author : John Neuberger
language : en
Publisher: American Mathematical Soc.
Release Date : 2004

Variational Methods Open Problems Recent Progress And Numerical Algorithms written by John Neuberger and has been published by American Mathematical Soc. this book supported file pdf, txt, epub, kindle and other format this book has been release on 2004 with Mathematics categories.

This volume contains the proceedings of the conference on Variational Methods: Open Problems, Recent Progress, and Numerical Algorithms. It presents current research in variational methods as applied to nonlinear elliptic PDE, although several articles concern nonlinear PDE that are nonvariational and/or nonelliptic. The book contains both survey and research papers discussing important open questions and offering suggestions on analytical and numerical techniques for solving those open problems. It is suitable for graduate students and research mathematicians interested in elliptic partial differential equations.

Topics In Operator Theory

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Author : Joseph A. Ball
language : en
Publisher: Springer Science & Business Media
Release Date : 2011-02-09

Topics In Operator Theory written by Joseph A. Ball 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 2011-02-09 with Mathematics categories.

This is the first volume of a collection of original and review articles on recent advances and new directions in a multifaceted and interconnected area of mathematics and its applications. It encompasses many topics in theoretical developments in operator theory and its diverse applications in applied mathematics, physics, engineering, and other disciplines. The purpose is to bring in one volume many important original results of cutting edge research as well as authoritative review of recent achievements, challenges, and future directions in the area of operator theory and its applications.

Ecole D Ete De Probabilites De Saint Flour

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Author : J. Bertoin
language : en
Publisher: Springer Science & Business Media
Release Date : 1999-11-17

Ecole D Ete De Probabilites De Saint Flour written by J. Bertoin 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 1999-11-17 with Mathematics categories.

Lecture Notes in Mathematics This series reports on new developments in mathematical research and teaching - quickly, informally and at a high level. The type of material considered for publication includes 1. Research monographs 2. Lectures on a new field or presentations of a new angle in a classical field 3. Summer schools and intensive courses on topics of current research Texts which are out of print but still in demand may also be considered. The timeliness of a manuscript is sometimes more important than its form, which might be preliminary or tentative. Details of the editorial policy can be found on the inside front-cover of a current volume. Manuscripts should be submitted in camera-ready form according to Springer-Verlag's specification: technical instructions will be sent on request. TEX macros may be found at: http://www.springer.de/math/authors/b-tex.html Select the version of TEX you use and then click on "Monographs". A subject index should be included. We recommend contacting the publisher or the series editors at an early stage of your project. Addresses are given on the inside back-cover.

Complex Analysis And Dynamical Systems Iii

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Author : Mark Lʹvovich Agranovskiĭ
language : en
Publisher: American Mathematical Soc.
Release Date : 2008

Complex Analysis And Dynamical Systems Iii written by Mark Lʹvovich Agranovskiĭ and has been published by American Mathematical Soc. this book supported file pdf, txt, epub, kindle and other format this book has been release on 2008 with Mathematics categories.

The papers in this volume cover a wide variety of topics in the geometric theory of functions of one and several complex variables, including univalent functions, conformal and quasiconformal mappings, minimal surfaces, and dynamics in infinite-dimensional spaces. In addition, there are several articles dealing with various aspects of approximation theory and partial differential equations. Taken together, the articles collected here provide the reader with a panorama of activity in complex analysis, drawn by a number of leading figures in the field.