DOLFIN: Automated finite element computing

By Anders Logg, Garth N. Wells. TOMS, 2010

836 citations recorded by the source corpus.

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 article 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.

Subfields: Computational Mechanics, Electrical and Electronic Engineering, Numerical Analysis

View Paper: https://www.semanticscholar.org/paper/066e817d512bc77109ecd2e2230bfed364ff2ef6

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In Computational Mechanics

In Electrical and Electronic Engineering

In Numerical Analysis

Citations in the corpus

Automated Solution of Differential Equations by the Finite Element Method: The FEniCS Book (2012, methodology): “In particular, a light-weight Python module, ASCoT (Rognes, 2009), constructed on top of DOLFIN (Logg and Wells, 2010), is described.”
trlib: a vector-free implementation of the GLTR method for iterative solution of the trust region problem (2016, methodology): “Here vectorial data is only considered as FEniCS-objects and no numerical data except of dot products is used of these objects.”
Firedrake (2015, background): “Previous work, most especially the Uniﬁed Form Language [Alnæs et al. 2014] employed by the FEniCS project [Logg et al. 2012; Logg and Wells 2010] enables scientists to express partial differential equations (PDEs) in a high productivity interpreted language close to the mathematics.”
Unified form language: A domain-specific language for weak formulations of partial differential equations (2012, methodology): “This is discussed in detail in Logg and Wells [24].”
Discrete approximations of the Föppl–Von Kármán shell model: From coarse to more refined models (2013, methodology): “The code makes use of the Fenics framework (Logg and Wells, 2010), an open source software distributed under the GNU-LGPL license.”
pyGIMLi: An open-source library for modelling and inversion in geophysics (2017, background): “…free, ﬂ exible, and cross-platform-compatible nature, which therefore makes it widely used in the (geo)scienti ﬁ c community (e.g., Guyer et al., 2009; Logg and Wells, 2010; P (cid:1) erez et al., 2011; Wellmann et al., 2012; Uieda et al., 2013; Cockett et al., 2015; Weigand and Kemna, 2016;…”
Automated Derivation of the Adjoint of High-Level Transient Finite Element Programs (2012, background): “These components include the Unified Form Language (UFL) [2, 1], the FEniCS Form Compiler (FFC) [26], and DOLFIN [33, 34].”
Topological derivatives applied to fluid flow channel design optimization problems (2016, methodology): “The local tensors are used by DOLFIN [29], a library that handles the communication between all the FEniCS modules.”