The Conjugate Gradient Algorithm For Finite Element Systems
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Author |
: Michal Krizek |
Publisher |
: Springer Science & Business Media |
Total Pages |
: 405 |
Release |
: 2012-12-06 |
ISBN-10 |
: 9783642185601 |
ISBN-13 |
: 3642185606 |
Rating |
: 4/5 (01 Downloads) |
Synopsis Conjugate Gradient Algorithms and Finite Element Methods by : Michal Krizek
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.
Author |
: James Albert Metzler |
Publisher |
: |
Total Pages |
: 354 |
Release |
: 1976 |
ISBN-10 |
: OCLC:7770038 |
ISBN-13 |
: |
Rating |
: 4/5 (38 Downloads) |
Synopsis The Conjugate Gradient Algorithm for Finite Element Systems by : James Albert Metzler
Author |
: Owe Axelsson |
Publisher |
: Springer |
Total Pages |
: 204 |
Release |
: 2006-11-14 |
ISBN-10 |
: 9783540467465 |
ISBN-13 |
: 3540467467 |
Rating |
: 4/5 (65 Downloads) |
Synopsis Preconditioned Conjugate Gradient Methods by : Owe Axelsson
Author |
: Josef Malek |
Publisher |
: SIAM |
Total Pages |
: 106 |
Release |
: 2014-12-22 |
ISBN-10 |
: 9781611973846 |
ISBN-13 |
: 1611973848 |
Rating |
: 4/5 (46 Downloads) |
Synopsis Preconditioning and the Conjugate Gradient Method in the Context of Solving PDEs by : Josef Malek
Preconditioning and the Conjugate Gradient Method in the Context of Solving PDEs is about the interplay between modeling, analysis, discretization, matrix computation, and model reduction. The authors link PDE analysis, functional analysis, and calculus of variations with matrix iterative computation using Krylov subspace methods and address the challenges that arise during formulation of the mathematical model through to efficient numerical solution of the algebraic problem. The book?s central concept, preconditioning of the conjugate gradient method, is traditionally developed algebraically using the preconditioned finite-dimensional algebraic system. In this text, however, preconditioning is connected to the PDE analysis, and the infinite-dimensional formulation of the conjugate gradient method and its discretization and preconditioning are linked together. This text challenges commonly held views, addresses widespread misunderstandings, and formulates thought-provoking open questions for further research.
Author |
: Mario Arioli |
Publisher |
: |
Total Pages |
: |
Release |
: 2003 |
ISBN-10 |
: OCLC:59270029 |
ISBN-13 |
: |
Rating |
: 4/5 (29 Downloads) |
Synopsis A Stopping Criterion for the Conjugate Gradient Algorithm in a Finite Element Method Framework by : Mario Arioli
Author |
: Loyce Adams |
Publisher |
: |
Total Pages |
: 36 |
Release |
: 1983 |
ISBN-10 |
: NASA:31769001171266 |
ISBN-13 |
: |
Rating |
: 4/5 (66 Downloads) |
Synopsis M-step Preconditioned Conjugate Gradient Methods by : Loyce Adams
Author |
: George T. Spetar |
Publisher |
: |
Total Pages |
: 78 |
Release |
: 1977 |
ISBN-10 |
: OCLC:3930773 |
ISBN-13 |
: |
Rating |
: 4/5 (73 Downloads) |
Synopsis Applications of the Conjugate Gradient Method to Finite Element Problems by : George T. Spetar
Author |
: Miloslav Feistauer |
Publisher |
: Springer Science & Business Media |
Total Pages |
: 873 |
Release |
: 2012-12-06 |
ISBN-10 |
: 9783642187759 |
ISBN-13 |
: 3642187757 |
Rating |
: 4/5 (59 Downloads) |
Synopsis Numerical Mathematics and Advanced Applications by : Miloslav Feistauer
These proceedings collect the major part of the lectures given at ENU MATH2003, the European Conference on Numerical Mathematics and Ad vanced Applications, held in Prague, Czech Republic, from 18 August to 22 August, 2003. The importance of numerical and computational mathematics and sci entific computing is permanently growing. There is an increasing number of different research areas, where numerical simulation is necessary. Let us men tion fluid dynamics, continuum mechanics, electromagnetism, phase transi tion, cosmology, medicine, economics, finance, etc. The success of applications of numerical methods is conditioned by changing its basic instruments and looking for new appropriate techniques adapted to new problems as well as new computer architectures. The ENUMATH conferences were established in order to provide a fo rum for discussion of current topics of numerical mathematics. They seek to convene leading experts and young scientists with special emphasis on con tributions from Europe. Recent results and new trends are discussed in the analysis of numerical algorithms as well as in their applications to challenging scientific and industrial problems. The first ENUMATH conference was organized in Paris in 1995, then the series continued by the conferences in Heidelberg 1997, Jyvaskyla 1999 and Ischia Porto 2001. It was a great pleasure and honour for the Czech numerical community that it was decided at Ischia Porto to organize the ENUMATH2003 in Prague. It was the first time when this conference crossed the former Iron Courtain and was organized in a postsocialist country.
Author |
: Hatfield Polytechnic. Numerical Optimisation Centre |
Publisher |
: |
Total Pages |
: 32 |
Release |
: 1982 |
ISBN-10 |
: OCLC:123320502 |
ISBN-13 |
: |
Rating |
: 4/5 (02 Downloads) |
Synopsis A Parallel Version of the Conjugate Gradient Algorithm for Finite Element Problems by : Hatfield Polytechnic. Numerical Optimisation Centre
Author |
: Granville Sewell |
Publisher |
: Springer Science & Business Media |
Total Pages |
: 163 |
Release |
: 2012-12-06 |
ISBN-10 |
: 9781468463316 |
ISBN-13 |
: 1468463314 |
Rating |
: 4/5 (16 Downloads) |
Synopsis Analysis of a Finite Element Method by : Granville Sewell
This text can be used for two quite different purposes. It can be used as a reference book for the PDElPROTRAN user· who wishes to know more about the methods employed by PDE/PROTRAN Edition 1 (or its predecessor, TWODEPEP) in solving two-dimensional partial differential equations. However, because PDE/PROTRAN solves such a wide class of problems, an outline of the algorithms contained in PDElPROTRAN is also quite suitable as a text for an introductory graduate level finite element course. Algorithms which solve elliptic, parabolic, hyperbolic, and eigenvalue partial differential equation problems are pre sented, as are techniques appropriate for treatment of singularities, curved boundaries, nonsymmetric and nonlinear problems, and systems of PDEs. Direct and iterative linear equation solvers are studied. Although the text emphasizes those algorithms which are actually implemented in PDEI PROTRAN, and does not discuss in detail one- and three-dimensional problems, or collocation and least squares finite element methods, for example, many of the most commonly used techniques are studied in detail. Algorithms applicable to general problems are naturally emphasized, and not special purpose algorithms which may be more efficient for specialized problems, such as Laplace's equation. It can be argued, however, that the student will better understand the finite element method after seeing the details of one successful implementation than after seeing a broad overview of the many types of elements, linear equation solvers, and other options in existence.