Automated Solution Of Differential Equations By The Finite Element Method


Automated Solution Of Differential Equations By The Finite Element Method
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Automated Solution Of Differential Equations By The Finite Element Method


Automated Solution Of Differential Equations By The Finite Element Method
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Author : Anders Logg
language : en
Publisher: Springer Science & Business Media
Release Date : 2012-02-24

Automated Solution Of Differential Equations By The Finite Element Method written by Anders Logg 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 2012-02-24 with Computers categories.


This book is a tutorial written by researchers and developers behind the FEniCS Project and explores an advanced, expressive approach to the development of mathematical software. The presentation spans mathematical background, software design and the use of FEniCS in applications. Theoretical aspects are complemented with computer code which is available as free/open source software. The book begins with a special introductory tutorial for beginners. Following are chapters in Part I addressing fundamental aspects of the approach to automating the creation of finite element solvers. Chapters in Part II address the design and implementation of the FEnicS software. Chapters in Part III present the application of FEniCS to a wide range of applications, including fluid flow, solid mechanics, electromagnetics and geophysics.



Introduction To Automated Modeling With Fenics


Introduction To Automated Modeling With Fenics
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Author : Larkin Ridgway Scott
language : en
Publisher:
Release Date : 2018

Introduction To Automated Modeling With Fenics written by Larkin Ridgway Scott and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 2018 with categories.




Numerical Solution Of Partial Differential Equations By The Finite Element Method


Numerical Solution Of Partial Differential Equations By The Finite Element Method
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Author : Claes Johnson
language : en
Publisher: Courier Corporation
Release Date : 2012-05-23

Numerical Solution Of Partial Differential Equations By The Finite Element Method written by Claes Johnson and has been published by Courier Corporation this book supported file pdf, txt, epub, kindle and other format this book has been release on 2012-05-23 with Mathematics categories.


An accessible introduction to the finite element method for solving numeric problems, this volume offers the keys to an important technique in computational mathematics. Suitable for advanced undergraduate and graduate courses, it outlines clear connections with applications and considers numerous examples from a variety of science- and engineering-related specialties.This text encompasses all varieties of the basic linear partial differential equations, including elliptic, parabolic and hyperbolic problems, as well as stationary and time-dependent problems. Additional topics include finite element methods for integral equations, an introduction to nonlinear problems, and considerations of unique developments of finite element techniques related to parabolic problems, including methods for automatic time step control. The relevant mathematics are expressed in non-technical terms whenever possible, in the interests of keeping the treatment accessible to a majority of students.



The Finite Element Method Theory Implementation And Applications


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.​



Finite Element Methods


Finite Element Methods
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Author : Jonathan Whiteley
language : en
Publisher: Springer
Release Date : 2017-01-26

Finite Element Methods written by Jonathan Whiteley and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2017-01-26 with Science categories.


This book presents practical applications of the finite element method to general differential equations. The underlying strategy of deriving the finite element solution is introduced using linear ordinary differential equations, thus allowing the basic concepts of the finite element solution to be introduced without being obscured by the additional mathematical detail required when applying this technique to partial differential equations. The author generalizes the presented approach to partial differential equations which include nonlinearities. The book also includes variations of the finite element method such as different classes of meshes and basic functions. Practical application of the theory is emphasised, with development of all concepts leading ultimately to a description of their computational implementation illustrated using Matlab functions. The target audience primarily comprises applied researchers and practitioners in engineering, but the book may also be beneficial for graduate students.



Solving Pdes In Python


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.



The Finite Element Method


The Finite Element Method
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Author : A. J. Davies
language : en
Publisher: OUP Oxford
Release Date : 2011-09-08

The Finite Element Method written by A. J. Davies and has been published by OUP Oxford this book supported file pdf, txt, epub, kindle and other format this book has been release on 2011-09-08 with Mathematics categories.


The finite element method is a technique for solving problems in applied science and engineering. The essence of this book is the application of the finite element method to the solution of boundary and initial-value problems posed in terms of partial differential equations. The method is developed for the solution of Poisson's equation, in a weighted-residual context, and then proceeds to time-dependent and nonlinear problems. The relationship with the variational approach is also explained. This book is written at an introductory level, developing all the necessary concepts where required. Consequently, it is well-placed to be used as a textbook for a course in finite elements for final year undergraduates, the usual place for studying finite elements. There are worked examples throughout and each chapter has a set of exercises with detailed solutions.



Introduction To The Tools Of Scientific Computing


Introduction To The Tools Of Scientific Computing
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Author : Einar Smith
language : en
Publisher: Springer Nature
Release Date : 2020-12-02

Introduction To The Tools Of Scientific Computing written by Einar Smith and has been published by Springer Nature this book supported file pdf, txt, epub, kindle and other format this book has been release on 2020-12-02 with Mathematics categories.


The book provides an introduction to common programming tools and methods in numerical mathematics and scientific computing. Unlike widely used standard approaches, it does not focus on any particular language but aims to explain the key underlying concepts. In general, new concepts are first introduced in the particularly user-friendly Python language and then transferred and expanded in various scientific programming environments from C / C ++, Julia and MATLAB to Maple. This includes different approaches to distributed computing. The fact that different languages are studied and compared also makes the book useful for mathematicians and practitioners trying to decide which programming language to use for which purposes.



Finite Element Methods And Their Applications


Finite Element Methods And Their Applications
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Author : Zhangxin Chen
language : en
Publisher: Springer Science & Business Media
Release Date : 2006-03-30

Finite Element Methods And Their Applications written by Zhangxin Chen 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 2006-03-30 with Science categories.


Introduce every concept in the simplest setting and to maintain a level of treatment that is as rigorous as possible without being unnecessarily abstract. Contains unique recent developments of various finite elements such as nonconforming, mixed, discontinuous, characteristic, and adaptive finite elements, along with their applications. Describes unique recent applications of finite element methods to important fields such as multiphase flows in porous media and semiconductor modelling. Treats the three major types of partial differential equations, i.e., elliptic, parabolic, and hyperbolic equations.



The Mathematical Foundations Of The Finite Element Method With Applications To Partial Differential Equations


The Mathematical Foundations Of The Finite Element Method With Applications To Partial Differential Equations
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Author : A. K. Aziz
language : en
Publisher: Academic Press
Release Date : 2014-05-10

The Mathematical Foundations Of The Finite Element Method With Applications To Partial Differential Equations written by A. K. Aziz and has been published by Academic Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2014-05-10 with Technology & Engineering categories.


The Mathematical Foundations of the Finite Element Method with Applications to Partial Differential Equations is a collection of papers presented at the 1972 Symposium by the same title, held at the University of Maryland, Baltimore County Campus. This symposium relates considerable numerical analysis involved in research in both theoretical and practical aspects of the finite element method. This text is organized into three parts encompassing 34 chapters. Part I focuses on the mathematical foundations of the finite element method, including papers on theory of approximation, variational principles, the problems of perturbations, and the eigenvalue problem. Part II covers a large number of important results of both a theoretical and a practical nature. This part discusses the piecewise analytic interpolation and approximation of triangulated polygons; the Patch test for convergence of finite elements; solutions for Dirichlet problems; variational crimes in the field; and superconvergence result for the approximate solution of the heat equation by a collocation method. Part III explores the many practical aspects of finite element method. This book will be of great value to mathematicians, engineers, and physicists.