Automated Solution of Differential Equations by the Finite Element Method: The FEniCS Book

@inproceedings{Logg2012AutomatedSO,
  title={Automated Solution of Differential Equations by the Finite Element Method: The FEniCS Book},
  author={Anders Logg and Kent-Andr{\'e} Mardal and Garth N. Wells},
  year={2012}
}
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. Followingare chapters in Part I addressing… Expand

Figures, Tables, and Topics from this paper

SOLVING ELECTROMAGNETIC WAVE PROPAGATION PROBLEMS USING FENICS
TLDR
The FEniCS software can easily be used to solve the Maxwell wave equation and with the help of the dolfin-adjoint library, also backward problems, such as inverse electromagnetic scattering, can be solved using this software. Expand
Automating the solution of PDEs on the sphere and other manifolds in FEniCS 1.2
Abstract. Differential equations posed over immersed manifolds are of particular importance in studying geophysical flows; for instance, ocean and atmosphere simulations crucially rely on theExpand
Automated Derivation of the Adjoint of High-Level Transient Finite Element Programs
TLDR
A new technique for deriving discrete adjoint and tangent linear models of a finite element model using the FEniCS finite element form compiler, which is significantly more efficient and automatic than standard algorithmic differentiation techniques. Expand
GRINS: A Multiphysics Framework Based on the libMesh Finite Element Library
TLDR
This work describes a flexible C++ software framework, built on the libMesh finite element library, designed to alleviate developer burden and provide easy access to modern computational algorithms, including quantity-of-interest-driven parallel adaptive mesh refinement on unstructured grids and adjoint-based sensitivities. Expand
Automated Solution of Partial Differential Equations with Discontinuities using the Partition of Unity Method
TLDR
The automatic code generation has been extended to support developing models for problems with discontinuities in the context of the FEniCS project, an open source project in the Automation of Computational Mathematical Modelling (ACMM). Expand
Automated derivation of the adjoint of high-level transient finite element programs
TLDR
The approach to automated adjoint derivation relies on run-time annotation of the temporal structure of the model, and employs the FEniCS finite element form compiler to automatically generate the low-level code for the derived models. Expand
FEniCS Framework in Geoscientific Applications
The FEniCS Project is an open source finite element framework for solving PDEs. The advantage of this framework is a tight connection between the mathematical model, the associated variationalExpand
Automatic differentiation for solid mechanics
TLDR
This paper uses automatic differentiation for stating and solving solid mechanics problems, and makes use of AD for directly obtaining the residual force vector and the tangent stiffness matrix of the problem, as the gradient and the Hessian of the free energy respectively. Expand
Periodic Table of the Finite Elements
The finite element method is one of the most powerful and widely applicable techniques for the numerical solution of partial differential equations and, therefore, for the simulation of the physicalExpand
Automating embedded analysis capabilities and managing software complexity in multiphysics simulation, Part II: Application to partial differential equations
TLDR
The implementation details for using the template-based generic programming approach for simulation and analysis of partial differential equations (PDEs) are described and several of the hurdles that have encountered are detailed. Expand
...
1
2
3
4
5
...

References

SHOWING 1-10 OF 394 REFERENCES
A FEniCS-Based Programming Framework for Modeling Turbulent Flow by the Reynolds-Averaged Navier-Stokes Equations
TLDR
The design and implementation of a flexible, programmable software framework for assisting with numerical experiments in computational turbulence and the impact of various linearizations on the convergence properties of nonlinear solvers for a Reynolds-averaged Navier–Stokes model are investigated. Expand
DOLFIN: Automated finite element computing
TLDR
A library aimed at automating the solution of partial differential equations using the finite element method, from which low-level code is automatically generated, compiled and seamlessly integrated with efficient implementations of computational meshes and high-performance linear algebra. Expand
Finite-Element Model for Modified Boussinesq Equations. I: Model Development
This paper and its companion paper describe the development of a finite-element model based on modified Boussinesq equations and the applications of the model to harbor resonance problems. This firstExpand
Automating the Finite Element Method
Abstract The finite element method can be viewed as a machine that automates the discretization of differential equations, taking as input a variational problem, a finite element and a mesh, andExpand
A finite element method for the two‐dimensional extended Boussinesq equations
A new numerical method for Nwogu's (ASCE Journal of Waterway, Port, Coastal and Ocean Engineering 1993; 119:618)two-dimensional extended Boussinesq equations is presented using a linear triangularExpand
Automated FEM discretizations for the Stokes equation
Current FEM software projects have made significant advances in various automated modeling techniques. We present some of the mathematical abstractions employed by these projects that allow a user toExpand
A numerical solution of the Navier-Stokes equations using the finite element technique
Abstract The finite element discretisation technique is used to effect a solution of the Navier- Stokes equations. Two methods of formulation are presented, and a comparison of the effeciency of theExpand
Computational Methods for Geodynamics
Written as both a textbook and a handy reference, this text deliberately avoids complex mathematics assuming only basic familiarity with geodynamic theory and calculus. Here, the authors have broughtExpand
Automated Modelling of Evolving Discontinuities
TLDR
The automated approximation of solutions to differential equations which involve discontinuities across evolving surfaces is addressed by exploring the scope for employing automated code generation techniques for modelling discontinUities. Expand
An Introduction to Multigrid Methods
These notes were written for an introductory course on the application of multigrid methods to elliptic and hyperbolic partial differential equations for engineers, physicists and appliedExpand
...
1
2
3
4
5
...