Isogeometric analysis with geometrically continuous functions on two-patch geometries
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.
2015
2015-10-15 05:57:55
1033
izogeometrična analiza, geometrijska zveznost, geometrijsko vzezne izogeometrične funkcije, biharmonična enačba, isogeometric analysis, geometric continuity, geometrically continuous isogeometric functions, biharmonic equation, multi-patch domain,
r6
Mario
Kapl
70
Vito
Vitrih
70
Bert
Jüttler
70
Katharina
Birner
70
ISSN
2
0898-1221
UDK
4
519.6
OceCobissID
13
15336965
DOI
15
10.1016/j.camwa.2015.04.004
COBISS.SI-ID
3
1537819588
0
Predstavitvena datoteka
2015-10-15 05:57:55