Isogeometric analysis with geometrically continuous functions on two-patch geometries

Kapl, Mario; Vitrih, Vito; Jüttler, Bert; Birner, Katharina

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Title:	Isogeometric analysis with geometrically continuous functions on two-patch geometries
Authors:	ID Kapl, Mario (Author) ID Vitrih, Vito (Author) ID Jüttler, Bert (Author) ID Birner, Katharina (Author)
Files:	http://ac.els-cdn.com/S089812211500173X/1-s2.0-S089812211500173X-main.pdf?_tid=94ebf26e-65c7-11e5-a690-00000aacb361&acdnat=1443434537_5c4ed1d7a1642c0eac8eaa8cb06546b8
Language:	English
Work type:	Not categorized
Typology:	1.01 - Original Scientific Article
Organization:	IAM - Andrej Marušič Institute
Abstract:	We study the linear space of Cs-smooth isogeometric functions defined on a multi-patch domain % % R2. We show that the construction of these functions is closely related to the concept of geometric continuity of surfaces, which has originated in geometric design. More precisely, the Cs-smoothness of isogeometric functions is found to be equivalent to geometric smoothness of the same order (Gs-smoothness) of their graph surfaces. This motivates us to call them Cs-smooth geometrically continuous isogeometric functions. We present a general framework to construct a basis and explore potential applications in isogeometric analysis. The space of C1-smooth geometrically continuous isogeometric functions on bilinearly parameterized two-patch domains is analyzed in more detail. Numerical experiments with bicubic and biquartic functions for performing L2 approximation and for solving Poisson%s equation and the biharmonic equation on two-patch geometries are presented and indicate optimal rates of convergence.
Keywords:	izogeometrična analiza, geometrijska zveznost, geometrijsko vzezne izogeometrične funkcije, biharmonična enačba, isogeometric analysis, geometric continuity, geometrically continuous isogeometric functions, biharmonic equation, multi-patch domain
Year of publishing:	2015
Number of pages:	str. 1518-1538
Numbering:	Vol. 70, iss. 7
PID:	20.500.12556/RUP-7159
ISSN:	0898-1221
UDC:	519.6
DOI:	10.1016/j.camwa.2015.04.004
COBISS.SI-ID:	1537819588
Publication date in RUP:	15.10.2015
Views:	4897
Downloads:	199
Metadata:
:	KAPL, Mario, VITRIH, Vito, JÜTTLER, Bert and BIRNER, Katharina, 2015, Isogeometric analysis with geometrically continuous functions on two-patch geometries. [online]. 2015. Vol. 70, no. 7, p. 1518–1538. [Accessed 3 April 2025]. DOI 10.1016/j.camwa.2015.04.004. Retrieved from: http://ac.els-cdn.com/S089812211500173X/1-s2.0-S089812211500173X-main.pdf?_tid=94ebf26e-65c7-11e5-a690-00000aacb361&acdnat=1443434537_5c4ed1d7a1642c0eac8eaa8cb06546b8 Copy citation

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