Variational Methods for Numerical Solution of Nonlinear Elliptic Problems
Published on 30. October 2015
Book
Paperback/Softback
481 pages
978-1-61197-377-8 (ISBN)
Description
Addresses computational methods that have proven efficient for the solution of a large variety of nonlinear elliptic problems. These methods can be applied to many problems in science and engineering, but this book focuses on their application to problems in continuum mechanics and physics.
This book differs from others on the topic by:
Presenting examples of the power and versatility of operator-splitting methods.
Providing a detailed introduction to alternating direction methods of multipliers and their applicability to the solution of nonlinear (possibly non-smooth) problems from science and engineering.
Showing that nonlinear least-squares methods, combined with operator-splitting and conjugate gradient algorithms, provide efficient tools for the solution of highly nonlinear problems.
This book differs from others on the topic by:
Presenting examples of the power and versatility of operator-splitting methods.
Providing a detailed introduction to alternating direction methods of multipliers and their applicability to the solution of nonlinear (possibly non-smooth) problems from science and engineering.
Showing that nonlinear least-squares methods, combined with operator-splitting and conjugate gradient algorithms, provide efficient tools for the solution of highly nonlinear problems.
More details
Series
Language
English
Place of publication
New York
United States
Target group
College/higher education
Professional and scholarly
Product notice
Paperback (trade)
Dimensions
Height: 250 mm
Width: 172 mm
Thickness: 28 mm
Weight
940 gr
ISBN-13
978-1-61197-377-8 (9781611973778)
Copyright in bibliographic data and cover images is held by Nielsen Book Services Limited or by the publishers or by their respective licensors: all rights reserved.
Schweitzer Classification
Person
Roland Glowinski is Cullen Professor of Mathematics at the University of Houston and an Emeritus Professor of the Universite Pierre et Marie Curie (Paris VI). He is a member of the French National Academy of Sciences, the French National Academy of Technology, and the Academia Europaea. He is also a Fellow of both SIAM and the AMS and past recipient of the Theodore von Karman Prize for the notable application of mathematics to mechanics and/or the engineering sciences.
Content
Preface
Chapter 1: On some variational problems in Hilbert spaces
Chapter 2: Iterative methods in Hilbert spaces
Chapter 3: Operator-splitting and alternating direction methods
Chapter 4: Augmented Lagrangians and alternating direction methods of multipliers
Chapter 5: Least-squares solution of linear and nonlinear problems in Hilbert spaces
Chapter 6: Obstacle problems and Bingham flow application to control
Chapter 7: Other nonlinear eigenvalue problems
Chapter 8: Eikonal equations
Chapter 9: Fully nonlinear elliptic problems
Epilogue
Bibliography
Author index
Subject index
Chapter 1: On some variational problems in Hilbert spaces
Chapter 2: Iterative methods in Hilbert spaces
Chapter 3: Operator-splitting and alternating direction methods
Chapter 4: Augmented Lagrangians and alternating direction methods of multipliers
Chapter 5: Least-squares solution of linear and nonlinear problems in Hilbert spaces
Chapter 6: Obstacle problems and Bingham flow application to control
Chapter 7: Other nonlinear eigenvalue problems
Chapter 8: Eikonal equations
Chapter 9: Fully nonlinear elliptic problems
Epilogue
Bibliography
Author index
Subject index