Automated Solution Of Differential Equations By The Finite Element Method PDF Download
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Author | : Anders Logg |
Publisher | : Springer Science & Business Media |
Total Pages | : 723 |
Release | : 2012-02-24 |
Genre | : Computers |
ISBN | : 3642230997 |
Download Automated Solution of Differential Equations by the Finite Element Method Book in PDF, ePub and Kindle
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 |
Total Pages | : 152 |
Release | : 2017-03-21 |
Genre | : Computers |
ISBN | : 3319524623 |
Download Solving PDEs in Python Book in PDF, ePub and Kindle
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 |
Total Pages | : 344 |
Release | : 2020-12-02 |
Genre | : Mathematics |
ISBN | : 3030608085 |
Download Introduction to the Tools of Scientific Computing Book in PDF, ePub and Kindle
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 | : |
Total Pages | : |
Release | : 2018 |
Genre | : |
ISBN | : 9781949133011 |
Download Introduction to Automated Modeling with FEniCS Book in PDF, ePub and Kindle
Author | : P. SESHU |
Publisher | : PHI Learning Pvt. Ltd. |
Total Pages | : 340 |
Release | : 2003-01-01 |
Genre | : Mathematics |
ISBN | : 8120323157 |
Download TEXTBOOK OF FINITE ELEMENT ANALYSIS Book in PDF, ePub and Kindle
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 | : L. Ridgway Scott |
Publisher | : |
Total Pages | : 390 |
Release | : 2018-05-31 |
Genre | : Computers |
ISBN | : 9781949133004 |
Download Introduction to Automated Modeling with Fenics Book in PDF, ePub and Kindle
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 | : Chuanmiao Chen |
Publisher | : World Scientific |
Total Pages | : 294 |
Release | : 1998 |
Genre | : Mathematics |
ISBN | : 9789810232634 |
Download Finite Element Methods for Integrodifferential Equations Book in PDF, ePub and Kindle
Recently, there has appeared a new type of evaluating partial differential equations with Volterra integral operators in various practical areas. Such equations possess new physical and mathematical properties. This monograph systematically discusses application of the finite element methods to numerical solution of integrodifferential equations. It will be useful for numerical analysts, mathematicians, physicists and engineers. Advanced undergraduates and graduate students should also find it beneficial.
Author | : Hans Petter Langtangen |
Publisher | : Springer Nature |
Total Pages | : 395 |
Release | : 2019-09-26 |
Genre | : Mathematics |
ISBN | : 3030237885 |
Download Introduction to Numerical Methods for Variational Problems Book in PDF, ePub and Kindle
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 | : Wolfgang Bangerth |
Publisher | : Birkhäuser |
Total Pages | : 216 |
Release | : 2013-11-11 |
Genre | : Mathematics |
ISBN | : 303487605X |
Download Adaptive Finite Element Methods for Differential Equations Book in PDF, ePub and Kindle
These Lecture Notes have been compiled from the material presented by the second author in a lecture series ('Nachdiplomvorlesung') at the Department of Mathematics of the ETH Zurich during the summer term 2002. Concepts of 'self adaptivity' in the numerical solution of differential equations are discussed with emphasis on Galerkin finite element methods. The key issues are a posteriori er ror estimation and automatic mesh adaptation. Besides the traditional approach of energy-norm error control, a new duality-based technique, the Dual Weighted Residual method (or shortly D WR method) for goal-oriented error estimation is discussed in detail. This method aims at economical computation of arbitrary quantities of physical interest by properly adapting the computational mesh. This is typically required in the design cycles of technical applications. For example, the drag coefficient of a body immersed in a viscous flow is computed, then it is minimized by varying certain control parameters, and finally the stability of the resulting flow is investigated by solving an eigenvalue problem. 'Goal-oriented' adaptivity is designed to achieve these tasks with minimal cost. The basics of the DWR method and various of its applications are described in the following survey articles: R. Rannacher [114], Error control in finite element computations. In: Proc. of Summer School Error Control and Adaptivity in Scientific Computing (H. Bulgak and C. Zenger, eds), pp. 247-278. Kluwer Academic Publishers, 1998. M. Braack and R. Rannacher [42], Adaptive finite element methods for low Mach-number flows with chemical reactions.
Author | : Mohammad Asadzadeh |
Publisher | : John Wiley & Sons |
Total Pages | : 352 |
Release | : 2020-08-27 |
Genre | : Mathematics |
ISBN | : 1119671663 |
Download An Introduction to the Finite Element Method for Differential Equations Book in PDF, ePub and Kindle
Master the finite element method with this masterful and practical volume An Introduction to the Finite Element Method (FEM) for Differential Equations provides readers with a practical and approachable examination of the use of the finite element method in mathematics. Author Mohammad Asadzadeh covers basic FEM theory, both in one-dimensional and higher dimensional cases. The book is filled with concrete strategies and useful methods to simplify its complex mathematical contents. Practically written and carefully detailed, An Introduction to the Finite Element Method covers topics including: An introduction to basic ordinary and partial differential equations The concept of fundamental solutions using Green's function approaches Polynomial approximations and interpolations, quadrature rules, and iterative numerical methods to solve linear systems of equations Higher-dimensional interpolation procedures Stability and convergence analysis of FEM for differential equations This book is ideal for upper-level undergraduate and graduate students in natural science and engineering. It belongs on the shelf of anyone seeking to improve their understanding of differential equations.