Journal
COMPUTER METHODS IN APPLIED MECHANICS AND ENGINEERING
Volume 253, Issue -, Pages 584-598Publisher
ELSEVIER SCIENCE SA
DOI: 10.1016/j.cma.2012.06.023
Keywords
Finite elements; Hierarchical b-splines; Subdivision schemes; Isogeometric analysis
Funding
- EPSRC [EP/G008531/1]
- EPSRC [EP/G008531/1] Funding Source: UKRI
- Engineering and Physical Sciences Research Council [EP/G008531/1] Funding Source: researchfish
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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. (C) 2012 Elsevier B.V. All rights reserved.
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