Isogeometric analysis with geometrically continuous functions on planar multi-patch geometries

Abstract

We generate a basis of the space of bicubic and biquartic C1-smooth geometrically continuous isogeometric functions on bilinear multi-patch domains Ω⊂R2. The basis functions are obtained by suitably combining C1-smooth geometrically continuous isogeometric functions on bilinearly parameterized two-patch domains (cf. [18]). They are described by simple explicit formulas for their spline coefficients.These C1-smooth isogeometric functions possess potential for applications in isogeometric analysis, which is demonstrated by several examples (such as the biharmonic equation). In particular, the numerical results indicate optimal approximation power.