Automated modelling of evolving discontinuities
type: Item
instance of: scholarly article
title: Automated modelling of evolving discontinuities
zbMATH Open document ID: 1461.65252
author: Mehdi Nikbakht
author: Garth N. Wells
published in: Algorithms
publication date: 2018-08-20T00:00:00Z
review text: Summary: 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.
Mathematics Subject Classification ID: 65N30
Mathematics Subject Classification ID: 74S05
zbMATH DE Number: 6920464
zbMATH Keywords: partition of unity
zbMATH Keywords: extended finite element method
zbMATH Keywords: fracture
zbMATH Keywords: automation
zbMATH Keywords: form compiler
describes a project that uses: DOLFIN
describes a project that uses: FEniCS
describes a project that uses: XFEM
MaRDI profile type: Publication
full work available at URL: https://doi.org/10.3390/a2031008
OpenAlex ID: W2051866751
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DOI: 10.3390/A2031008
description: scientific article; zbMATH DE number 6920464