Journal
COMPUTER METHODS IN APPLIED MECHANICS AND ENGINEERING
Volume 328, Issue -, Pages 147-174Publisher
ELSEVIER SCIENCE SA
DOI: 10.1016/j.cma.2017.08.017
Keywords
Isogeometric Analysis; Local refinement; (Truncated) hierarchical B-splines; Bezier extraction
Funding
- TUM Institute for Advanced Study - German Excellence Initiative
- European Union Seventh Framework Programme [291763]
- German Research Foundation (DFG) [RA 624/22, RA 624/27, SPP 1748]
- Fondazione Cariplo - Regione Lombardia through the project Verso nuovi strumenti di simulazione super veloci ed accurati basati sull'analisi isogeometrica, within the program RST - rafforzamento
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One of the main topics of research on Isogeometric Analysis is local refinement. Among the various techniques currently studied and developed, one of the most appealing, referred to as hierarchical B-Splines, consists of defining a suitable set of basis functions on different hierarchical levels. This strategy can also be improved, for example to recover partition of unity, resorting to a truncation operation, giving rise to the so-called truncated hierarchical B-Splines. Despite its conceptual simplicity, implementing the hierarchical definition of shape functions into an existing code can be rather involved. In this work we present a simple way to bring the hierarchical isogeometric concept closer to a standard finite element formulation. Practically speaking, the hierarchy of functions and knot spans is flattened into a sequence of elements being equipped with a standard single-level basis. In fact, the proposed multi-level extraction is a generalization of the classical Bezier extraction and analogously offers a standard element structure to the hierarchical overlay of functions. Moreover, this approach is suitable for an extension to non-linear problems and for a parallel implementation. The multi-level extraction is presented as a general concept that can be applied to different kinds of refinements and basis functions. Finally, few basic algorithms to compute the local multi-level extraction operator for knot insertion on spline spaces are outlined and compared, and some numerical examples are presented. (C) 2017 Elsevier B.V. All rights reserved.
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