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Conjugate Gradient Algorithms and Finite Element Methods

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Cover of 'Conjugate Gradient Algorithms and Finite Element Methods'

Table of Contents

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    Book Overview
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    Chapter 1 The Founders of the Conjugate Gradient Method
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    Chapter 2 Conjugate Gradients and Finite Elements — a Golden Jubilee
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    Chapter 3 Geometric Interpretations of Conjugate Gradient and Related Methods
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    Chapter 4 The Convergence of Krylov Methods and Ritz Values
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    Chapter 5 An Application of the Shermann-Morrison Formula to the GMRES Method
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    Chapter 6 A Parallel CG Solver Based on Domain Decomposition and Non-Smooth Aggregation
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    Chapter 7 Deflation in Preconditioned Conjugate Gradient Methods for Finite Element Problems
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    Chapter 8 Nonsmooth Equation Method for Nonlinear Nonconvex Optimization
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    Chapter 9 Nonstandard Nonobtuse Refinements of Planar Triangulations
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    Chapter 10 Acute Versus Nonobtuse Tetrahedralizations
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    Chapter 11 A Posteriori Error Estimation of “Quantities of Interest” on “Quantity-Adapted” Meshes
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    Chapter 12 Inversion of Block-Tridiagonal Matrices and Nonnegativity Preservation in the Numerical Solution of Linear Parabolic PDEs
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    Chapter 13 On the Nonnegativity Conservation in Semidiscrete Parabolic Problems
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    Chapter 14 Iterative Solution Methods of the Maxwell Equations Using Staggered Grid Spatial Discretization
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    Chapter 15 Iterative Solution of Linear Variational Problems in Hilbert Spaces: Some Conjugate Gradients Success Stories
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    Chapter 16 On the Applicationn of Preconditioning Operators for Nonlinear Elliptic Problems
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    Chapter 17 On a Conjugate Gradient/Newton/Penalty Method for the Solution of Obstacle Problems. Application to the Solution of an Eikonal System with Dirichlet Boundary Conditions
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    Chapter 18 The Use of Bilinear Rectangular Elements in Reconstruction of Panoramic Images
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    Chapter 19 Finite Element Discretization and Iterative Solution Techniques for Multiphase Flows in Gas-Liquid Reactors
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    Chapter 20 Implicit Flux-Corrected Transport Algorithm for Finite Element Simulation of the Compressible Euler Equations
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    Chapter 21 Application of the PCG Method in Solution of a Nuclear Reactor Criticality Problem
Attention for Chapter 15: Iterative Solution of Linear Variational Problems in Hilbert Spaces: Some Conjugate Gradients Success Stories
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Chapter title
Iterative Solution of Linear Variational Problems in Hilbert Spaces: Some Conjugate Gradients Success Stories
Chapter number 15
Book title
Conjugate Gradient Algorithms and Finite Element Methods
Published by
Springer, Berlin, Heidelberg, January 2004
DOI 10.1007/978-3-642-18560-1_15
Book ISBNs
978-3-64-262159-8, 978-3-64-218560-1
Authors

Roland Glowinski, Serguei Lapin

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