Isogeometric analysis with geometrically continuous functions on two-patch geometries

Mario Kapl (Author), Vito Vitrih (Author), Bert Jüttler (Author), Katharina Birner (Author)

Abstract

We study the linear space of ▫$C^s$▫-smooth isogeometric functions defined on a multi-patch domain ▫$\Omega \subset \mathbb{R}^2$▫. 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 ▫$C^s$▫-smoothness of isogeometric functions is found to be equivalent to geometric smoothness of the same order (▫$G^s$▫-smoothness) of their graph surfaces. This motivates us to call them ▫$C^s$▫-smooth geometrically continuous isogeometric functions. We present a general framework to construct a basis and explore potential applications in isogeometric analysis. The space of ▫$C^1$▫-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 ▫$L^2$▫ 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;

Data

Language:	English
Year of publishing:	2015
Typology:	1.01 - Original Scientific Article
Organization:	UP - University of Primorska
UDC:	519.65
COBISS:	1537819588
ISSN:	0898-1221
Views:	2963
Downloads:	192
Average score:	0 (0 votes)
Metadata:

Other data

Secondary language:	Unknown
Type (COBISS):	Not categorized
Pages:	str. 1518-1538
Volume:	ǂVol. ǂ70
Issue:	ǂiss. ǂ7
Chronology:	2015
DOI:	10.1016/j.camwa.2015.04.004
ID:	9058102