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BOOK EXCERPT:
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.
Product Details :
Genre |
: Mathematics |
Author |
: John Neuberger |
Publisher |
: Springer Science & Business Media |
Release |
: 2009-12-01 |
File |
: 287 Pages |
ISBN-13 |
: 9783642040405 |
eBook Download
BOOK EXCERPT:
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.
Product Details :
Genre |
: Mathematics |
Author |
: John W. Neuberger |
Publisher |
: |
Release |
: 1997 |
File |
: 164 Pages |
ISBN-13 |
: STANFORD:36105020674383 |
eBook Download
BOOK EXCERPT:
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.
Product Details :
Genre |
: Mathematics |
Author |
: john neuberger |
Publisher |
: Springer |
Release |
: 2009-11-10 |
File |
: 287 Pages |
ISBN-13 |
: 9783642040412 |
eBook Download
BOOK EXCERPT:
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.
Product Details :
Genre |
: Mathematics |
Author |
: john neuberger |
Publisher |
: Springer |
Release |
: 2006-11-13 |
File |
: 150 Pages |
ISBN-13 |
: 9783540695943 |
eBook Download
BOOK EXCERPT:
Product Details :
Genre |
: |
Author |
: John William Neuberger |
Publisher |
: |
Release |
: 1997 |
File |
: 149 Pages |
ISBN-13 |
: 3642040578 |
eBook Download
BOOK EXCERPT:
Product Details :
Genre |
: Numerical analysis |
Author |
: Society for Industrial and Applied Mathematics |
Publisher |
: |
Release |
: 2004-07 |
File |
: 924 Pages |
ISBN-13 |
: UCR:31210016063354 |
eBook Download
BOOK EXCERPT:
Product Details :
Genre |
: Mathematics |
Author |
: |
Publisher |
: |
Release |
: 2006 |
File |
: 860 Pages |
ISBN-13 |
: UOM:39015067268279 |
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BOOK EXCERPT:
Product Details :
Genre |
: Mathematics |
Author |
: American Mathematical Society |
Publisher |
: |
Release |
: 2008 |
File |
: 784 Pages |
ISBN-13 |
: CORNELL:31924099658993 |
eBook Download
BOOK EXCERPT:
Product Details :
Genre |
: Mathematics |
Author |
: |
Publisher |
: |
Release |
: 2009 |
File |
: 716 Pages |
ISBN-13 |
: UCSD:31822036938819 |
eBook Download
BOOK EXCERPT:
Product Details :
Genre |
: Mathematics |
Author |
: Eötvös Loránd Tudományegyetem |
Publisher |
: |
Release |
: 2000 |
File |
: 180 Pages |
ISBN-13 |
: UCAL:B4484463 |