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Automating the finite element method

Anders Logg (Institutionen för matematiska vetenskaper, matematik)
Archives of Computational Methods in Engineering (1134-3060). Vol. 14 (2007), 2, p. 93-138.
[Artikel, refereegranskad vetenskaplig]

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, and producing as output a system of discrete equations. However, the generality of the framework provided by the finite element method is seldom reflected in implementations (realizations), which are often specialized and can handle only a small set of variational problems and finite elements (but are typically parametrized over the choice of mesh). This paper reviews ongoing research in the direction of a complete automation of the finite element method. In particular, this work discusses algorithms for the efficient and automatic computation of a system of discrete equations from a given variational problem, finite element and mesh. It is demonstrated that by automatically generating and compiling efficient low-level code, it is possible to parametrize a finite element code over variational problem and finite element in addition to the mesh.



Denna post skapades 2014-01-05. Senast ändrad 2014-09-29.
CPL Pubid: 191162

 

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Institutioner (Chalmers)

Institutionen för matematiska vetenskaper, matematik (2005-2016)

Ämnesområden

Matematik
Beräkningsmatematik

Chalmers infrastruktur