Domain Decomposition And Iterative Refinement Methods For Mixed Finite Element Discretisations Of Elliptic Problems Classic Reprint
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Domain Decomposition And Iterative Refinement Methods For Mixed Finite Element Discretisations Of Elliptic Problems Classic Reprint
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Author : Tarek P. Mathew
language : en
Publisher: Forgotten Books
Release Date : 2017-11-20
Domain Decomposition And Iterative Refinement Methods For Mixed Finite Element Discretisations Of Elliptic Problems Classic Reprint written by Tarek P. Mathew and has been published by Forgotten Books this book supported file pdf, txt, epub, kindle and other format this book has been release on 2017-11-20 with Mathematics categories.
Excerpt from Domain Decomposition and Iterative Refinement Methods for Mixed Finite Element Discretisations of Elliptic Problems In this Chapter, we present the relevent background about saddle point formula tions of elliptic problems, and mixed finite element methods using the raviart-thomas spaces. We then discuss an extension theorem for the raviart-thomas finite element spaces, which we use later in establishing bounds for the rate of convergence of the domain decomposition methods. A section containing some background on iterative methods, is also included. In Chapter 2, we discuss algorithms involving subdomains with overlap, such as the classical Schwarz alternating method, cf. Lions and the additive Schwarz method, as studied by Dryja and Widlund We present proofs of convergenceof these iterative methods when applied to the mixed finite element case, and also show that the rate of convergence is independent of the mesh parmeter h. We also present numerical results of tests using these methods with many subdomains and a certain coarse mesh model problem, which improves the rate of convergence. The results indicate a rate of convergence, which is independent of the mesh parameter h and even the number of subdomains. We have also tested the methods on problems in which the discontinuity in the coefficients of the elliptic operator is large. Such large variations in the coefficients occur in certain applications involving flow in porous media. The rate of convergence remains independent of the jump in the discontinuity, but the accuracy of the pressure deteriorates. See the section on numerical results, in Chapter 2. About the Publisher Forgotten Books publishes hundreds of thousands of rare and classic books. Find more at www.forgottenbooks.com This book is a reproduction of an important historical work. Forgotten Books uses state-of-the-art technology to digitally reconstruct the work, preserving the original format whilst repairing imperfections present in the aged copy. In rare cases, an imperfection in the original, such as a blemish or missing page, may be replicated in our edition. We do, however, repair the vast majority of imperfections successfully; any imperfections that remain are intentionally left to preserve the state of such historical works.
Domain Decomposition And Iterative Refinement Methods For Mixed Finite Element Discretisations Of Elliptic Problems
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Author : Tarek P Mathew
language : en
Publisher: Legare Street Press
Release Date : 2022-10-27
Domain Decomposition And Iterative Refinement Methods For Mixed Finite Element Discretisations Of Elliptic Problems written by Tarek P Mathew and has been published by Legare Street Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2022-10-27 with History categories.
This work has been selected by scholars as being culturally important, and is part of the knowledge base of civilization as we know it. This work is in the "public domain in the United States of America, and possibly other nations. Within the United States, you may freely copy and distribute this work, as no entity (individual or corporate) has a copyright on the body of the work. Scholars believe, and we concur, that this work is important enough to be preserved, reproduced, and made generally available to the public. We appreciate your support of the preservation process, and thank you for being an important part of keeping this knowledge alive and relevant.
Mathematical Reviews
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Author :
language : en
Publisher:
Release Date : 1999
Mathematical Reviews written by and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1999 with Mathematics categories.
Parallel Numerical Algorithms
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Author : David E. Keyes
language : en
Publisher: Springer Science & Business Media
Release Date : 2012-12-06
Parallel Numerical Algorithms written by David E. Keyes 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.
In this volume, designed for computational scientists and engineers working on applications requiring the memories and processing rates of large-scale parallelism, leading algorithmicists survey their own field-defining contributions, together with enough historical and bibliographical perspective to permit working one's way to the frontiers. This book is distinguished from earlier surveys in parallel numerical algorithms by its extension of coverage beyond core linear algebraic methods into tools more directly associated with partial differential and integral equations - though still with an appealing generality - and by its focus on practical medium-granularity parallelism, approachable through traditional programming languages. Several of the authors used their invitation to participate as a chance to stand back and create a unified overview, which nonspecialists will appreciate.
The Finite Element Method Theory Implementation And Applications
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Author : Mats G. Larson
language : en
Publisher: Springer Science & Business Media
Release Date : 2013-01-13
The Finite Element Method Theory Implementation And Applications written by Mats G. Larson 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 2013-01-13 with Computers categories.
This book gives an introduction to the finite element method as a general computational method for solving partial differential equations approximately. Our approach is mathematical in nature with a strong focus on the underlying mathematical principles, such as approximation properties of piecewise polynomial spaces, and variational formulations of partial differential equations, but with a minimum level of advanced mathematical machinery from functional analysis and partial differential equations. In principle, the material should be accessible to students with only knowledge of calculus of several variables, basic partial differential equations, and linear algebra, as the necessary concepts from more advanced analysis are introduced when needed. Throughout the text we emphasize implementation of the involved algorithms, and have therefore mixed mathematical theory with concrete computer code using the numerical software MATLAB is and its PDE-Toolbox. We have also had the ambition to cover some of the most important applications of finite elements and the basic finite element methods developed for those applications, including diffusion and transport phenomena, solid and fluid mechanics, and also electromagnetics.
Numerical Approximation Of Partial Differential Equations
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Author : Alfio Quarteroni
language : en
Publisher: Springer Science & Business Media
Release Date : 2009-02-11
Numerical Approximation Of Partial Differential Equations written by Alfio Quarteroni 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 2009-02-11 with Mathematics categories.
Everything is more simple than one thinks but at the same time more complex than one can understand Johann Wolfgang von Goethe To reach the point that is unknown to you, you must take the road that is unknown to you St. John of the Cross This is a book on the numerical approximation ofpartial differential equations (PDEs). Its scope is to provide a thorough illustration of numerical methods (especially those stemming from the variational formulation of PDEs), carry out their stability and convergence analysis, derive error bounds, and discuss the algorithmic aspects relative to their implementation. A sound balancing of theoretical analysis, description of algorithms and discussion of applications is our primary concern. Many kinds of problems are addressed: linear and nonlinear, steady and time-dependent, having either smooth or non-smooth solutions. Besides model equations, we consider a number of (initial-) boundary value problems of interest in several fields of applications. Part I is devoted to the description and analysis of general numerical methods for the discretization of partial differential equations. A comprehensive theory of Galerkin methods and its variants (Petrov Galerkin and generalized Galerkin), as wellas ofcollocationmethods, is devel oped for the spatial discretization. This theory is then specified to two numer ical subspace realizations of remarkable interest: the finite element method (conforming, non-conforming, mixed, hybrid) and the spectral method (Leg endre and Chebyshev expansion).
Solving Pdes In Python
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Author : Hans Petter Langtangen
language : en
Publisher: Springer
Release Date : 2017-03-21
Solving Pdes In Python written by Hans Petter Langtangen and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2017-03-21 with Computers categories.
This book offers a concise and gentle introduction to finite element programming in Python based on the popular FEniCS software library. Using a series of examples, including the Poisson equation, the equations of linear elasticity, the incompressible Navier–Stokes equations, and systems of nonlinear advection–diffusion–reaction equations, it guides readers through the essential steps to quickly solving a PDE in FEniCS, such as how to define a finite variational problem, how to set boundary conditions, how to solve linear and nonlinear systems, and how to visualize solutions and structure finite element Python programs. This book is open access under a CC BY license.
Numerical Models For Differential Problems
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Author : Alfio Quarteroni
language : en
Publisher: Springer Science & Business
Release Date : 2014-04-25
Numerical Models For Differential Problems written by Alfio Quarteroni and has been published by Springer Science & Business this book supported file pdf, txt, epub, kindle and other format this book has been release on 2014-04-25 with Mathematics categories.
In this text, we introduce the basic concepts for the numerical modelling of partial differential equations. We consider the classical elliptic, parabolic and hyperbolic linear equations, but also the diffusion, transport, and Navier-Stokes equations, as well as equations representing conservation laws, saddle-point problems and optimal control problems. Furthermore, we provide numerous physical examples which underline such equations. We then analyze numerical solution methods based on finite elements, finite differences, finite volumes, spectral methods and domain decomposition methods, and reduced basis methods. In particular, we discuss the algorithmic and computer implementation aspects and provide a number of easy-to-use programs. The text does not require any previous advanced mathematical knowledge of partial differential equations: the absolutely essential concepts are reported in a preliminary chapter. It is therefore suitable for students of bachelor and master courses in scientific disciplines, and recommendable to those researchers in the academic and extra-academic domain who want to approach this interesting branch of applied mathematics.
The Mathematics Of Reservoir Simulation
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Author : Richard E. Ewing
language : en
Publisher: SIAM
Release Date : 1983-01-01
The Mathematics Of Reservoir Simulation written by Richard E. Ewing and has been published by SIAM this book supported file pdf, txt, epub, kindle and other format this book has been release on 1983-01-01 with Science categories.
The emergence of complex enhanced recovery procedures in the field of hydrocarbon extraction techniques has emphasized the need for sophisticated mathematical tools, capable of modeling intricate chemical and physical phenomena and sharply changing fluid interfaces. This volume explains which problems need to be addressed, why they are difficult, what has been done previously to treat these difficulties, and which new techniques appear to possess potential for obtaining good simulation results.
Some Domain Decomposition And Iterative Refinement Algorithms For Elliptic Finite Element Problems Classic Reprint
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Author : Olof Widlund
language : en
Publisher: Forgotten Books
Release Date : 2018-02-11
Some Domain Decomposition And Iterative Refinement Algorithms For Elliptic Finite Element Problems Classic Reprint written by Olof Widlund and has been published by Forgotten Books this book supported file pdf, txt, epub, kindle and other format this book has been release on 2018-02-11 with Mathematics categories.
Excerpt from Some Domain Decomposition and Iterative Refinement Algorithms for Elliptic Finite Element Problems In the second section of this paper, we introduce a framework similar to Lions' and also an additive parallel) version of the Schwarz algorithm. While Lions considered the continuous problems, we work consistently with conforming finite element approximations; cf. About the Publisher Forgotten Books publishes hundreds of thousands of rare and classic books. Find more at www.forgottenbooks.com This book is a reproduction of an important historical work. Forgotten Books uses state-of-the-art technology to digitally reconstruct the work, preserving the original format whilst repairing imperfections present in the aged copy. In rare cases, an imperfection in the original, such as a blemish or missing page, may be replicated in our edition. We do, however, repair the vast majority of imperfections successfully; any imperfections that remain are intentionally left to preserve the state of such historical works.