Conjugate Gradient Algorithms And Finite Element Methods
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Conjugate Gradient Algorithms And Finite Element Methods
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Author : Michal Krizek
language : en
Publisher: Springer Science & Business Media
Release Date : 2012-12-06
Conjugate Gradient Algorithms And Finite Element Methods written by Michal Krizek and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2012-12-06 with Science categories.
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.
A Finite Element Conjugate Gradient Fft Method For Scattering
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Author : National Aeronautics and Space Administration (NASA)
language : en
Publisher: Createspace Independent Publishing Platform
Release Date : 2018-06-28
A Finite Element Conjugate Gradient Fft Method For Scattering written by National Aeronautics and Space Administration (NASA) and has been published by Createspace Independent Publishing Platform this book supported file pdf, txt, epub, kindle and other format this book has been release on 2018-06-28 with categories.
An extension of a two dimensional formulation is presented for a three dimensional body of revolution. With the introduction of a Fourier expansion of the vector electric and magnetic fields, a coupled two dimensional system is generated and solved via the finite element method. An exact boundary condition is employed to terminate the mesh and the fast fourier transformation (FFT) is used to evaluate the boundary integrals for low O(n) memory demand when an iterative solution algorithm is used. By virtue of the finite element method, the algorithm is applicable to structures of arbitrary material composition. Several improvements to the two dimensional algorithm are also described. These include: (1) modifications for terminating the mesh at circular boundaries without distorting the convolutionality of the boundary integrals; (2) the development of nonproprietary mesh generation routines for two dimensional applications; (3) the development of preprocessors for interfacing SDRC IDEAS with the main algorithm; and (4) the development of post-processing algorithms based on the public domain package GRAFIC to generate two and three dimensional gray level and color field maps. Collins, Jeffery D. and Zapp, John and Hsa, Chang-Yu and Volakis, John L. Unspecified Center ...
Data Parallel Algorithms For The Finite Element Method
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Author : Kapil K. Mathur
language : en
Publisher:
Release Date : 1990
Data Parallel Algorithms For The Finite Element Method written by Kapil K. Mathur and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1990 with Finite element method categories.
Domain Decomposition Methods For Nonconforming Finite Element Discretizations
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Author : Jinsheng Gu
language : en
Publisher: Nova Publishers
Release Date : 1999
Domain Decomposition Methods For Nonconforming Finite Element Discretizations written by Jinsheng Gu and has been published by Nova Publishers this book supported file pdf, txt, epub, kindle and other format this book has been release on 1999 with Mathematics categories.
Domain decomposition refers to numerical methods for obtaining solutions of scientific and engineering problems by combining solutions to problems posed on physical subdomains, or, more generally, by combining solutions to appropriately constructed subproblems. It has been a subject of intense interest recently because of its suitability for implementation on high performance computer architectures. It is well known that the nonconforming finite elements are widely used in and effective for the solving of partial differential equations derived from mechanics and engineering, because they have fewer degrees of freedom, simpler basis functions and better convergence behavior. But, there has been no extensive study of domain decomposition methods with nonconforming finite elements which lack the global continuity. Therefore, a rather systematic investigation on domain decomposition methods with nonconforming elements is of great significance and this is what the present book achieves. The theoretical breakthrough is the establishment of a series of essential estimates, especially the extension theorems for nonconforming elements, which play key roles in domain decomposition analysis. There are also many originalities in the design of the domain decomposition algorithms for the nonconforming finite element discretizations, according to the features of the nonconforming elements. The existing domain decomposition methods developed in the conforming finite element discrete case can be revised properly and extended to the nonconforming finite element discrete case correspondingly. These algorithms, nonoverlap or overlap, are as efficient as their counterparts in the conforming cases, and even easier in implementation.
Preconditioning And The Conjugate Gradient Method In The Context Of Solving Pdes
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Author : Josef Malek
language : en
Publisher: SIAM
Release Date : 2014-12-22
Preconditioning And The Conjugate Gradient Method In The Context Of Solving Pdes written by Josef Malek and has been published by SIAM this book supported file pdf, txt, epub, kindle and other format this book has been release on 2014-12-22 with Mathematics categories.
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.
Understanding And Implementing The Finite Element Method
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Author : Mark S. Gockenbach
language : en
Publisher: SIAM
Release Date : 2006-01-01
Understanding And Implementing The Finite Element Method written by Mark S. Gockenbach and has been published by SIAM this book supported file pdf, txt, epub, kindle and other format this book has been release on 2006-01-01 with Finite element method categories.
Understanding and Implementing the Finite Element Method Mark S. Gockenbach "Upon completion of this book a student or researcher would be well prepared to employ finite elements for an application problem or proceed to the cutting edge of research in finite element methods. The accuracy and the thoroughness of the book are excellent." --Anthony Kearsley, research mathematician, National Institute of Standards and Technology The infinite element method is the most powerful general-purpose technique for computing accurate solutions to partial differential equations. Understanding and Implementing the Finite Element Method is essential reading for those interested in understanding both the theory and the implementation of the finite element method for equilibrium problems. This book contains a thorough derivation of the finite element equations as well as sections on programming the necessary calculations, solving the finite element equations, and using a posteriori error estimates to produce validated solutions. Accessible introductions to advanced topics, such as multigrid solvers, the hierarchical basis conjugate gradient method, and adaptive mesh generation, are provided. Each chapter ends with exercises to help readers master these topics.
Numerical Methods For Mixed Finite Element Problems
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Author : Jean Deteix
language : en
Publisher: Springer Nature
Release Date : 2022-09-24
Numerical Methods For Mixed Finite Element Problems written by Jean Deteix and has been published by Springer Nature this book supported file pdf, txt, epub, kindle and other format this book has been release on 2022-09-24 with Mathematics categories.
This book focuses on iterative solvers and preconditioners for mixed finite element methods. It provides an overview of some of the state-of-the-art solvers for discrete systems with constraints such as those which arise from mixed formulations. Starting by recalling the basic theory of mixed finite element methods, the book goes on to discuss the augmented Lagrangian method and gives a summary of the standard iterative methods, describing their usage for mixed methods. Here, preconditioners are built from an approximate factorisation of the mixed system. A first set of applications is considered for incompressible elasticity problems and flow problems, including non-linear models. An account of the mixed formulation for Dirichlet’s boundary conditions is then given before turning to contact problems, where contact between incompressible bodies leads to problems with two constraints. This book is aimed at graduate students and researchers in the field of numerical methods and scientific computing.
Analysis Of A Finite Element Method
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Author : Granville Sewell
language : en
Publisher: Springer Science & Business Media
Release Date : 2012-12-06
Analysis Of A Finite Element Method written by Granville Sewell and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2012-12-06 with Mathematics categories.
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.
Handbook Of Numerical Analysis
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Author : Philippe G. Ciarlet
language : en
Publisher: Gulf Professional Publishing
Release Date : 1990
Handbook Of Numerical Analysis written by Philippe G. Ciarlet and has been published by Gulf Professional Publishing this book supported file pdf, txt, epub, kindle and other format this book has been release on 1990 with Numerical analysis categories.
Includes following subjects: Solution of equations in Rn, Finite difference methods, Finite element methods, Techniques of scientific computing, Optimization theory and systems science, Numerical methods for fluids, Numerical methods for solids, Specific applications
Finite Element Methods In Cad
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Author : Jean Claude Sabonnadiere
language : en
Publisher: Springer Science & Business Media
Release Date : 2012-12-06
Finite Element Methods In Cad written by Jean Claude Sabonnadiere and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2012-12-06 with Computers categories.
The finite element method (FEM) has been understood, at least in principle, for more than 50 years. The integral formulation on which it is based has been known for a longer time (thanks to the work of Galerkin, Ritz, Courant and Hilbert,1.4 to mention the most important). However, the method could not be applied in a practical way since it involved the solution of a large number of linear or non-linear algebraic equations. Today it is quite common, with the aid of computers, to solve non-linear algebraic problems of several thousand equations. The necessary numerical methods and programming techniques are now an integral part of the teaching curriculum in most engineering schools. Mechanical engineers, confronted with very complicated structural problems, were the first to take advantage of advanced computational methods and high level languages (FORTRAN) to transform the mechanical models into algebraic equations (1956). In recent times (1960), the FEM has been studied by applied mathematicians and, having received rigorous treatment, has become a part of the more general study of partial differential equations, gradually replacing the finite difference method which had been considered the universal tool to solve these types of problems.