Paper Info
Title
Automated Modelling Of Evolving Discontinuities
Abstract
The automated approximation of solutions to differential equations which involve discontinuities across evolving surfaces is addressed. Finite element technology has developed to the point where it is now possible to model evolving discontinuities independently of the underlying mesh, which is particularly useful in simulating failure of solids. However, the approach remains tedious to program, particularly in the case of coupled problems where a variety of finite element bases are employed and where a mixture of continuous and discontinuous fields may be used. We tackle this point by exploring the scope for employing automated code generation techniques for modelling discontinuities. Function spaces and variational forms are defined in a language that resembles mathematical notation, and computer code for modelling discontinuities is automatically generated. Principles underlying the approach are elucidated and a number of two-and three-dimensional examples for different equations are presented.
Year
DOI
Venue
2009
10.3390/a2031008
ALGORITHMS
Keywords
Field
DocType
partition of unity, extended finite element method, fracture, automation, form compiler
Mathematical notation,Differential equation,Partition of unity,Mathematical optimization,Classification of discontinuities,Computer science,Source code,Algorithm,Extended finite element method,Code generation,Finite element method
Journal
Volume
Issue
ISSN
2
3
1999-4893
Citations 
PageRank 
References 
3
0.71
2
Authors
2
Name
Order
Citations
PageRank
Mehdi Nikbakht130.71
Garth N. Wells220220.08