DOLFIN: Automated Finite Element Computing
Anders Logg,Garth N. Wells +1 more
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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.Abstract:
We describe here a library aimed at automating the solution of partial differential equations using the finite element method. By employing novel techniques for automated code generation, the library combines a high level of expressiveness with efficient computation. Finite element variational forms may be expressed in near mathematical notation, from which low-level code is automatically generated, compiled and seamlessly integrated with efficient implementations of computational meshes and high-performance linear algebra. Easy-to-use object-oriented interfaces to the library are provided in the form of a C++ library and a Python module. This paper discusses the mathematical abstractions and methods used in the design of the library and its implementation. A number of examples are presented to demonstrate the use of the library in application code.read more
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Book
Automated Solution of Differential Equations by the Finite Element Method: The FEniCS Book
TL;DR: 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.
Journal ArticleDOI
Firedrake: automating the finite element method by composing abstractions
Florian Rathgeber,David A. Ham,Lawrence Mitchell,Michael Lange,Fabio Luporini,Andrew T. T. McRae,Gheorghe-Teodor Bercea,Graham Markall,Paul H. J. Kelly +8 more
TL;DR: Firedrake adopts the domain-specific language for the finite element method of the FEniCS project, but with a pure Python runtime-only implementation centred on the composition of several existing and new abstractions for particular aspects of scientific computing.
Journal ArticleDOI
Automated Derivation of the Adjoint of High-Level Transient Finite Element Programs
TL;DR: 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.
Posted Content
Unified Form Language: A domain-specific language for weak formulations of partial differential equations
TL;DR: The Unified Form Language is presented, which is a domain-specific language for representing weak formulations of partial differential equations with a view to numerical approximation and generates abstract syntax tree representations of variational problems, which are used by other software libraries to generate concrete low-level implementations.
Journal ArticleDOI
Algorithms and data structures for massively parallel generic adaptive finite element codes
TL;DR: This work develops scalable algorithms and data structures for generic finite element methods that consider the parallel distribution of mesh data, global enumeration of degrees of freedom, constraints, and postprocessing, and removes the bottlenecks that typically limit large-scale adaptive finite element analyses.
References
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Franco Brezzi,Michel Fortin +1 more
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Mixed finite elements in ℝ 3
TL;DR: In this article, the authors present two families of non-conforming finite elements, built on tetrahedrons or on cubes, which are respectively conforming in the spacesH(curl) and H(div).
Journal ArticleDOI
Conforming and nonconforming finite element methods for solving the stationary Stokes equations I
M. Crouzeix,P.-A. Raviart +1 more
TL;DR: Both conforming and nonconforming finite element methods are studied and various examples of simplicial éléments well suited for the numerical treatment of the incompressibility condition are given.