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Isogeometric analysis with geometrically continuous functions on two-patch geometries
Bert Jüttler, Vito Vitrih, Mario Kapl, Katharina Birner, 2015, original scientific article

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.
Found in: ključnih besedah
Summary of found: ...izogeometrična analiza, geometrijska zveznost, geometrijsko vzezne izogeometrične funkcije, biharmonična enačba,...
Keywords: izogeometrična analiza, geometrijska zveznost, geometrijsko vzezne izogeometrične funkcije, biharmonična enačba, isogeometric analysis, geometric continuity, geometrically continuous isogeometric functions, biharmonic equation, multi-patch domain
Published: 15.10.2015; Views: 1324; Downloads: 112
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