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Conjugate Gradient Algorithms and Finite Element Methods : Scientific Computation - Michel Krizek

Conjugate Gradient Algorithms and Finite Element Methods

Scientific Computation

By: Michel Krizek (Editor), P. Neittaanmaki (Editor), R. Glowinski (Editor), Sergey Korotov (Editor)

Hardcover Published: 1st July 2004
ISBN: 9783540213192
Number Of Pages: 384

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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.

The founders of the conjugate gradient methodp. 3
Conjugate gradients and finite elements - a golden jubileep. 11
Geometric interpretations of conjugate gradient and related methodsp. 25
The convergence of Krylov methods and Ritz valuesp. 47
An application of the Shermann-Morrison formula to the GMRES methodp. 69
A parallel CG solver based on domain decomposition and non-smooth aggregationp. 93
Deflation in preconditioned conjugate gradient methods for finite element problemsp. 103
Nonsmooth equation method for nonlinear nonconvex optimizationp. 131
Nonstandard nonobtuse refinements of planar triangulationsp. 149
Acute versus nonobtuse tetrahedralizationsp. 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 PDEsp. 185
On the nonnegativity conservation in semidiscrete parabolic problemsp. 197
Iterative solution methods of the Maxwell equations using staggered grid spatial discretizationp. 211
Iterative solution of linear variational problems in Hilbert spaces : some conjugate gradients success storiesp. 223
On the application of preconditioning operators for nonlinear elliptic problemsp. 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 conditionsp. 263
The use of bilinear rectangular elements in reconstruction of panoramic imagesp. 287
Finite element discretization and iterative solution techniques for multiphase flows in gas-liquid reactorsp. 297
Implicit flux-corrected transport algorithm for finite element simulation of the compressible euler equationsp. 325
Application of the PCG method in solution of a nuclear reactor criticality problemp. 355
Table of Contents provided by Blackwell. All Rights Reserved.

ISBN: 9783540213192
ISBN-10: 3540213198
Series: Scientific Computation
Audience: Professional
Format: Hardcover
Language: English
Number Of Pages: 384
Published: 1st July 2004
Publisher: Springer-Verlag Berlin and Heidelberg Gmbh & Co. Kg
Country of Publication: DE
Dimensions (cm): 23.5 x 15.5  x 1.91
Weight (kg): 0.84