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Automated Modelling of Evolving Discontinuities
Faculty of Civil Engineering and Geosciences, Delft University of Technology, Stevinweg 1, 2628 CN Delft, The Netherlands
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
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.
Keywords: partition of unity; extended finite element method; fracture; automation; form compiler
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MDPI and ACS Style
Nikbakht, M.; Wells, G.N. Automated Modelling of Evolving Discontinuities. Algorithms 2009, 2, 1008-1030.
Nikbakht M, Wells GN. Automated Modelling of Evolving Discontinuities. Algorithms. 2009; 2(3):1008-1030.
Nikbakht, Mehdi; Wells, Garth N. 2009. "Automated Modelling of Evolving Discontinuities." Algorithms 2, no. 3: 1008-1030.