Automated Solution of Differential Equations by the Finite Element Method PDF Download
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Author: Anders Logg
Publisher: Springer Science & Business Media
ISBN: 3642230997
Category : Computers
Languages : en
Pages : 731
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Book Description
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.
Author: Anders Logg
Publisher: Springer Science & Business Media
ISBN: 3642230997
Category : Computers
Languages : en
Pages : 731
Get Book
Book Description
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.
Author: Hans Petter Langtangen
Publisher: Springer
ISBN: 3319524623
Category : Computers
Languages : en
Pages : 152
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Book Description
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.
Author: Einar Smith
Publisher: Springer Nature
ISBN: 3030608085
Category : Mathematics
Languages : en
Pages : 344
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Book Description
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.
Author: Larkin Ridgway Scott
Publisher:
ISBN: 9781949133011
Category :
Languages : en
Pages :
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Book Description
Author: L. Ridgway Scott
Publisher:
ISBN: 9781949133004
Category : Computers
Languages : en
Pages : 390
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Book Description
Introduction to Automated Modeling with FEniCS exploressolution of partial differential equations via the finite element method. It illustrates the use of automated softwaregeneration via the FEniCS Project systems. The book reviews most common types of partial differential equations arising in technical simulation. It is ideal for engineers and for computational and applied mathematicians.
Author: P. SESHU
Publisher: PHI Learning Pvt. Ltd.
ISBN: 8120323157
Category : Mathematics
Languages : en
Pages : 340
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Book Description
Designed for a one-semester course in Finite Element Method, this compact and well-organized text presents FEM as a tool to find approximate solutions to differential equations. This provides the student a better perspective on the technique and its wide range of applications. This approach reflects the current trend as the present-day applications range from structures to biomechanics to electromagnetics, unlike in conventional texts that view FEM primarily as an extension of matrix methods of structural analysis. After an introduction and a review of mathematical preliminaries, the book gives a detailed discussion on FEM as a technique for solving differential equations and variational formulation of FEM. This is followed by a lucid presentation of one-dimensional and two-dimensional finite elements and finite element formulation for dynamics. The book concludes with some case studies that focus on industrial problems and Appendices that include mini-project topics based on near-real-life problems. Postgraduate/Senior undergraduate students of civil, mechanical and aeronautical engineering will find this text extremely useful; it will also appeal to the practising engineers and the teaching community.
Author: Mats G. Larson
Publisher: Springer Science & Business Media
ISBN: 3642332870
Category : Computers
Languages : en
Pages : 403
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Book Description
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.
Author: Hans Petter Langtangen
Publisher: Springer Nature
ISBN: 3030237885
Category : Mathematics
Languages : en
Pages : 395
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Book Description
This textbook teaches finite element methods from a computational point of view. It focuses on how to develop flexible computer programs with Python, a programming language in which a combination of symbolic and numerical tools is used to achieve an explicit and practical derivation of finite element algorithms. The finite element library FEniCS is used throughout the book, but the content is provided in sufficient detail to ensure that students with less mathematical background or mixed programming-language experience will equally benefit. All program examples are available on the Internet.
Author: Jonathan Whiteley
Publisher: Springer
ISBN: 3319499718
Category : Science
Languages : en
Pages : 232
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Book Description
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.
Author: A. J. Davies
Publisher: OUP Oxford
ISBN: 0191630349
Category : Mathematics
Languages : en
Pages : 312
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Book Description
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.
