Automated Solution of Differential Equations by the Finite Element Method

Author: Anders Logg
Publisher: Springer Science & Business Media
ISBN: 3642230997
Format: PDF
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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.

Automated Solution of Differential Equations by the Finite Element Method

Author: Anders Logg
Publisher: Springer
ISBN: 9783662508336
Format: PDF, Mobi
Download Now
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.

Automated Solution of Differential Equations by the Finite Element Method the FEniCS Project 2011

Author: The FEniCS Project
Publisher: Bukupedia
ISBN:
Format: PDF, Docs
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The FEniCS Project set out in 2003 with the idea to automate the solution of mathematical models based on differential equations. Initially, the FEniCS Project consisted of two libraries: DOLFIN and FIAT. Since then, the project has grown and now consists of the core components DOLFIN, FFC, FIAT, Instant, UFC and UFL. Other FEniCS components and applications described in this book are SyFi/SFC, FErari, AScot, Unicorn, CBC.Block, CBC.RANS, CBC.Solve and DOLFWAVE. Editor note: Check that we are not missing any applications/components. This book is written by researchers and developers behind the FEniCS Project. The presentation spans mathematical background, software design and the use of FEniCS in applications. The mathematical framework is outlined in Part I, the implementation of central components is described in Part II, while Part III concerns a wide range of applications. New users of FEniCS may find the tutorial included as the opening chapter particularly useful. Feedback on this book is welcome, and can be given at https://launchpad.net/fenics-book. Use the Launchpad system to file bug reports if you find errors in the text. For more information about the FEniCS Project, access to the software presented in this book, documentation, articles and presentations, visit the FEniCS Project web site at http://www.fenicsproject.org. Some of the chapters in this book are accompanied by supplementary material in the form of code examples. These code examples can be downloaded from http://www.fenicsproject.org/book. Editor note: GNW/KAM: Comment on code license. AL: Which code license? Anders Logg, Kent-Andre Mardal and Garth N. Wells Oslo and Cambridge, June 2011

The Finite Element Method Theory Implementation and Applications

Author: Mats G. Larson
Publisher: Springer Science & Business Media
ISBN: 3642332870
Format: PDF, Docs
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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.​

Parallel Processing and Applied Mathematics

Author: Roman Wyrzykowski
Publisher: Springer
ISBN: 3319321498
Format: PDF, ePub
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This two-volume set LNCS 9573 and LNCS 9574 constitutes the refereed proceedings of the 11th International Conference of Parallel Processing and Applied Mathematics, PPAM 2015, held in Krakow, Poland, in September 2015.The 111 revised full papers presented in both volumes were carefully reviewed and selected from 196 submissions. The focus of PPAM 2015 was on models, algorithms, and software tools which facilitate efficient and convenient utilization of modern parallel and distributed computing architectures, as well as on large-scale applications, including big data problems.

Software for Exascale Computing SPPEXA 2013 2015

Author: Hans-Joachim Bungartz
Publisher: Springer
ISBN: 3319405284
Format: PDF, Docs
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The research and its outcomes presented in this collection focus on various aspects of high-performance computing (HPC) software and its development which is confronted with various challenges as today's supercomputer technology heads towards exascale computing. The individual chapters address one or more of the research directions (1) computational algorithms, (2) system software, (3) application software, (4) data management and exploration, (5) programming, and (6) software tools. The collection thereby highlights pioneering research findings as well as innovative concepts in exascale software development that have been conducted under the umbrella of the priority programme "Software for Exascale Computing" (SPPEXA) of the German Research Foundation (DFG) and that have been presented at the SPPEXA Symposium, Jan 25-27 2016, in Munich. The book has an interdisciplinary appeal: scholars from computational sub-fields in computer science, mathematics, physics, or engineering will find it of particular interest.

Treatise on Geophysics

Author:
Publisher: Elsevier
ISBN: 0444538038
Format: PDF, Docs
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Treatise on Geophysics, Second Edition, is a comprehensive and in-depth study of the physics of the Earth beyond what any geophysics text has provided previously. Thoroughly revised and updated, it provides fundamental and state-of-the-art discussion of all aspects of geophysics. A highlight of the second edition is a new volume on Near Surface Geophysics that discusses the role of geophysics in the exploitation and conservation of natural resources and the assessment of degradation of natural systems by pollution. Additional features include new material in the Planets and Moon, Mantle Dynamics, Core Dynamics, Crustal and Lithosphere Dynamics, Evolution of the Earth, and Geodesy volumes. New material is also presented on the uses of Earth gravity measurements. This title is essential for professionals, researchers, professors, and advanced undergraduate and graduate students in the fields of Geophysics and Earth system science. Comprehensive and detailed coverage of all aspects of geophysics Fundamental and state-of-the-art discussions of all research topics Integration of topics into a coherent whole

Solving PDEs in Python

Author: Hans Petter Langtangen
Publisher: Springer
ISBN: 3319524623
Format: PDF, Docs
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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.

Solving Hyperbolic Equations with Finite Volume Methods

Author: M. Elena Vázquez-Cendón
Publisher: Springer
ISBN: 3319147846
Format: PDF, Mobi
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Finite volume methods are used in numerous applications and by a broad multidisciplinary scientific community. The book communicates this important tool to students, researchers in training and academics involved in the training of students in different science and technology fields. The selection of content is based on the author’s experience giving PhD and master courses in different universities. In the book the introduction of new concepts and numerical methods go together with simple exercises, examples and applications that contribute to reinforce them. In addition, some of them involve the execution of MATLAB codes. The author promotes an understanding of common terminology with a balance between mathematical rigor and physical intuition that characterizes the origin of the methods. This book aims to be a first contact with finite volume methods. Once readers have studied it, they will be able to follow more specific bibliographical references and use commercial programs or open source software within the framework of Computational Fluid Dynamics (CFD).