CUED Publications database

A subdivision-based implementation of the hierarchical b-spline finite element method

Bornemann, PB and Cirak, F (2013) A subdivision-based implementation of the hierarchical b-spline finite element method. Computer Methods in Applied Mechanics and Engineering, 253. pp. 584-598. ISSN 0045-7825

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Abstract

A novel technique is presented to facilitate the implementation of hierarchical b-splines and their interfacing with conventional finite element implementations. The discrete interpretation of the two-scale relation, as common in subdivision schemes, is used to establish algebraic relations between the basis functions and their coefficients on different levels of the hierarchical b-spline basis. The subdivision projection technique introduced allows us first to compute all element matrices and vectors using a fixed number of same-level basis functions. Their subsequent multiplication with subdivision matrices projects them, during the assembly stage, to the correct levels of the hierarchical b-spline basis. The proposed technique is applied to convergence studies of linear and geometrically nonlinear problems in one, two and three space dimensions. © 2012 Elsevier B.V.

Item Type: Article
Uncontrolled Keywords: Finite elements Hierarchical b-splines Isogeometric analysis Subdivision schemes
Subjects: UNSPECIFIED
Divisions: Div D > Structures
Depositing User: Cron Job
Date Deposited: 07 Mar 2014 11:20
Last Modified: 08 Dec 2014 02:33
DOI: 10.1016/j.cma.2012.06.023