UID:
almahu_9947367860302882
Format:
1 online resource (361 p.)
ISBN:
1-281-98489-2
,
9786611984892
,
0-08-087536-X
Series Statement:
Studies in mathematics and its applications ; v. 15
Uniform Title:
Méthodes de Lagrangien augmenté.
Content:
The purpose of this volume is to present the principles of the Augmented Lagrangian Method, together with numerous applications of this method to the numerical solution of boundary-value problems for partial differential equations or inequalities arising in Mathematical Physics, in the Mechanics of Continuous Media and in the Engineering Sciences.
Note:
Translation of: Methodes de Lagrangien augmente.
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Front Cover; Augmented Lagrangian Methods: Applications to the Numerical Solution of Boundary-Value Problems; Copyright Page; Table of Contents; Chapter 1. Augmented Lagrangian Methods in Quadratic Programming; 1. Principles of the Method; 2. A First Algorithm for Saddle-Point Calculation; 3. Variable Step-Length Algorithms . Conjugate Gradient Method; 4. On Certain Variants of the Methods of Section 2 : Introduction of a Relaxation Parameter ; Method of Arrow-Hurwicz; 5. Miscellaneous Remarks and Discussion; Chapter 2. Application to the Stokes and Navier-Stokes Equations; 1. Introduction
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2. Discretisation of the Stokes Problern3. Algorithms and Discussion of Results; 4. Navier - Stokes Equations, Steady-State Nonlinear Case; 5. Variants and Approximations of the Basic Algorithm of Section 4; 6. Navier-Stokes Equations. Time-Dependent Case; 7. General Discussion on Chapter II; Chapter 3. On Decomposition-Coordination Methods Using an Augmented Lagrangian; 1. Introduction; 2. Investigation of Problem (P) and of the Saddle-Points of L and L; 3. Description of the Algorithms; 4. Convergence of ALG1; 5. Convergence of ALG2; 6. Application to Some Nonlinear Problems
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7. Application to Nonlinear Programming Problems8. General Discussion on Chapter III; Chapter 4. Numerical Solution of Mildly Nonlinear Problems by Augmented Lagrangian Methods; 1. Introduction; 2. A Class of Mildly Nonlinear Elliptic Problems; 3. Augmented Lagrangian and Decomposition of the Problem (2.5),(2.6); 4. Algorithms for Solution of the Approximate Problem (2.13) . Discussion; 5. Numerical Experiments; 6. Some Remarks on Hybrid Methods; 7. General Discussion on Chapter IV; Chapter 5. Application to the Solution of Strongly Nonlinear Second-Order Boundary Value Problems
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1. Introduction2. General Framework of the Problems in Chapter V; 3. A Class of Nonlinear Dirichlet Problems; 4. A Magneto-Static Problem; 5. Calculation of Subsonic and Transonic Potential Flows; 6. Further applications; 7. Discussion on Chapter V; Chapter 6. Application of Algorithm ALG2 to a two Dimensional elastoplasticity Problem; Introduction; 1. The Continuous Problem; 2. The Problem ( P); 3. Approximation by Finite Elements; 4. Application of Algorithm ALG2; 5. Convergence of Algorithm ALG2; 6. Numerical Application; 7. Discussion
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Chapter 7. Application to the Numerical Solution of the two Dimensional Flow of Incompressible Viscoplastic Fluids1. General Notes. Synopsis; 2. Formulation of Bingham Flows Using the Velocity and the Pressure; 3. Formulation of Bingham Flows using A Stream Function; 4. Approximation of the Steady-State Problem; 5. Approximation of the Evolution Problem (3.7); 6. Solution of (4.1) (5.2) by Augmented Lagrangian Methods; 7. Numerical Experiments; Chapter 8. Application to the Solution of Finite Nonlinear Elasticity Problems; 1. General Notes . Synopsis
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2. Decomposition of Variational Problems. Associated Algorithms.
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English
Additional Edition:
ISBN 0-444-86680-9
Language:
English
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