Conjugate Gradient Algorithms and Finite Element Methods

By: M. Krizek (Editor), P. Neittaanmaki (Editor), R. Glowinski (Editor)

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Hardcover | 11 June 2004

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404 Pages

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23.5 x 15.88 x 1.91

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The position taken in this collection of pedagogically written essays is that conjugate gradient algorithms and finite element methods complement each other extremely well.

Via their combinations practitioners have been able to solve complicated, direct and inverse, multidemensional problems modeled by ordinary or partial differential equations and inequalities, not necessarily linear, optimal control and optimal design being part of these problems.

The aim of this book is to present both methods in the context of complicated problems modeled by linear and nonlinear partial differential equations, to provide an in-depth discussion on their implementation aspects. The authors show that conjugate gradient methods and finite element methods apply to the solution of real-life problems. They address graduate students as well as experts in scientific computing.

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You Can Find This Book In

Non-Fiction Computing & I.T.Computer Programming & Software Development Algorithms & Data Structures Mathematics Calculus & Mathematical Analysis Differential Calculus & Equations Applied Mathematics Science Physics Mathematical Physics Classical Mathematics

Fluid Mechanics Engineering & Technology Technology in General Engineering in General

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Paperback

Published: 1st November 2012

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The founders of the conjugate gradient method	p. 3
Conjugate gradients and finite elements - a golden jubilee	p. 11
Geometric interpretations of conjugate gradient and related methods	p. 25
The convergence of Krylov methods and Ritz values	p. 47
An application of the Shermann-Morrison formula to the GMRES method	p. 69
A parallel CG solver based on domain decomposition and non-smooth aggregation	p. 93
Deflation in preconditioned conjugate gradient methods for finite element problems	p. 103
Nonsmooth equation method for nonlinear nonconvex optimization	p. 131
Nonstandard nonobtuse refinements of planar triangulations	p. 149
Acute versus nonobtuse tetrahedralizations	p. 161
A posteriori eror estimation of "quantities of interest" on "quantity-adapted meshes"	p. 171
Inversion of block-tridiagonal matrices and nonnegativity preservation in the numerical solution of linear parabolic PDEs	p. 185
On the nonnegativity conservation in semidiscrete parabolic problems	p. 197
Iterative solution methods of the Maxwell equations using staggered grid spatial discretization	p. 211
Iterative solution of linear variational problems in Hilbert spaces : some conjugate gradients success stories	p. 223
On the application of preconditioning operators for nonlinear elliptic problems	p. 247
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	p. 263
The use of bilinear rectangular elements in reconstruction of panoramic images	p. 287
Finite element discretization and iterative solution techniques for multiphase flows in gas-liquid reactors	p. 297
Implicit flux-corrected transport algorithm for finite element simulation of the compressible euler equations	p. 325
Application of the PCG method in solution of a nuclear reactor criticality problem	p. 355
Table of Contents provided by Blackwell. All Rights Reserved.

Conjugate Gradient Algorithms and Finite Element Methods

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Hardcover

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