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Automated Solution of Differential Equations by the Finite Element Method

The FEniCS Book

  • Textbook
  • © 2012

Overview

Editors:
  1. Anders Logg

    1. Simula Research Laboratory, Lysaker, Norway

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    You can also search for this editor in PubMed   Google Scholar

  2. Kent-Andre Mardal

    1. Simula Research Laboratory, University of Oslo, Lysaker, Norway

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    You can also search for this editor in PubMed   Google Scholar

  3. Garth Wells

    1. , Department of Engineering, University of Cambridge, Cambridge, United Kingdom

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  • Unique synthesis of theory and computer code
  • Takes readers from an introductory tutorial through to cutting-edge research in scientific computing
  • Demonstrates a modern software approach to solving problems spanning fluid flow, solid mechanics, electromagnetics and geophysics
  • Includes supplementary material: sn.pub/extras

Part of the book series: Lecture Notes in Computational Science and Engineering (LNCSE, volume 84)

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Table of contents (36 chapters)

  1. Front Matter

    Pages I-XIII
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  2. A FEniCS tutorial

    • Hans Petter Langtangen
    Pages 1-73

  3. Methodology

    1. Front Matter

      Pages 75-75
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    2. The finite element method

      • Robert C. Kirby, Anders Logg
      Pages 77-94

    3. Common and unusual finite elements

      • Robert C. Kirby, Anders Logg, Marie E. Rognes, Andy R. Terrel
      Pages 95-119

    4. Constructing general reference finite elements

      • Robert C. Kirby, Kent-Andre Mardal
      Pages 121-132

    5. Finite element variational forms

      • Robert C. Kirby, Anders Logg
      Pages 133-140

    6. Finite element assembly

      • Anders Logg, Kent-Andre Mardal, Garth N. Wells
      Pages 141-146

    7. Quadrature representation of finite element variational forms

      • Kristian B. Ølgaard, Garth N. Wells
      Pages 147-158

    8. Tensor representation of finite element variational forms

      • Robert C. Kirby, Anders Logg
      Pages 159-162

    9. Discrete optimization of finite element matrix evaluation

      • Robert C. Kirby, Matthew Gregg Knepley, Anders Logg, L. Ridgway Scott, Andy R. Terrel
      Pages 163-169

  4. Implementation

    1. Front Matter

      Pages 171-171
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    2. DOLFIN: a C++/Python finite element library

      • Anders Logg, Garth N. Wells, Johan Hake
      Pages 173-225

    3. FFC: the FEniCS form compiler

      • Anders Logg, Kristian B. Ølgaard, Marie E. Rognes, Garth N. Wells
      Pages 227-238

    4. FErari: an optimizing compiler for variational forms

      • Robert C. Kirby, Anders Logg
      Pages 239-246

    5. FIAT: numerical construction of finite element basis functions

      • Robert C. Kirby
      Pages 247-255

    6. Instant: just-in-time compilation of C/C++ in Python

      • Ilmar M. Wilbers, Kent-Andre Mardal, Martin S. Alnæs
      Pages 257-272

    7. SyFi and SFC: symbolic finite elements and form compilation

      • Martin Sandve Alnæs, Kent-Andre Mardal
      Pages 273-282

    8. UFC: a finite element code generation interface

      • Martin Sandve Alnæs, Anders Logg, Kent-Andre Mardal
      Pages 283-302

    9. UFL: a finite element form language

      • Martin Sandve Alnæs
      Pages 303-338
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Keywords

About this book

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.

Editors and Affiliations

  • Simula Research Laboratory, Lysaker, Norway

    Anders Logg

  • Simula Research Laboratory, University of Oslo, Lysaker, Norway

    Kent-Andre Mardal

  • , Department of Engineering, University of Cambridge, Cambridge, United Kingdom

    Garth Wells

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