Isogeometric analysis with geometrically continuous functions on two-patch geometries

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

Povzetek

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.

Ključne besede

izogeometrična analiza;geometrijska zveznost;geometrijsko vzezne izogeometrične funkcije;biharmonična enačba;isogeometric analysis;geometric continuity;geometrically continuous isogeometric functions;biharmonic equation;multi-patch domain;

Podatki

Jezik:	Angleški jezik
Leto izida:	2015
Tipologija:	1.01 - Izvirni znanstveni članek
Organizacija:	UP - Univerza na Primorskem
UDK:	519.65
COBISS:	1537819588
ISSN:	0898-1221
Št. ogledov:	2963
Št. prenosov:	192
Ocena:	0 (0 glasov)
Metapodatki:

Ostali podatki

Sekundarni jezik:	Neznan jezik
Vrsta dela (COBISS):	Delo ni kategorizirano
Strani:	str. 1518-1538
Letnik:	ǂVol. ǂ70
Zvezek:	ǂiss. ǂ7
Čas izdaje:	2015
DOI:	10.1016/j.camwa.2015.04.004
ID:	9058102