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Algorithms 2009, 2(3), 1008-1030; doi:10.3390/a2031008

Automated Modelling of Evolving Discontinuities

1 Faculty of Civil Engineering and Geosciences, Delft University of Technology, Stevinweg 1, 2628 CN Delft, The Netherlands 2 Department of Engineering, University of Cambridge, Trumpington Street, Cambridge CB2 1PZ, UK
* Author to whom correspondence should be addressed.
Received: 7 May 2009 / Accepted: 7 August 2009 / Published: 18 August 2009
(This article belongs to the Special Issue Numerical Simulation of Discontinuities in Mechanics)
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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.
Keywords: partition of unity; extended finite element method; fracture; automation; form compiler partition of unity; extended finite element method; fracture; automation; form compiler
This is an open access article distributed under the Creative Commons Attribution License (CC BY) which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

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Nikbakht, M.; Wells, G.N. Automated Modelling of Evolving Discontinuities. Algorithms 2009, 2, 1008-1030.

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