Such constructions possess properties that make them suitable for performing both computational analysis and geometric modeling.Ībstract = "With the aim of a seamless integration with Computer-Aided Design, Isogeometric Analysis has been proposed by Hughes et al.
The third is a polar construction from Toshniwal et al. (2017c), uses a specific singular construction (the D-patch construction) at extraordinary points. (2016), is based on the concept of geometric continuity, well-known in geometric design. In this chapter we review three different methods to construct C 1 isogeometric spaces on multi-patch domains or unstructured quadrilateral meshes. Smooth splines yield two important benefits when compared to C 0 piecewise polynomial approximations: superior accuracy and stability, and the possibility to directly discretize high-order differential equations, such as the ones arising in thin-shell theory, in fracture models, in phase-field based multiphase flows, and in geometric flows on surfaces. Indeed, isogeometric analysis is based on splines, the same functions that are adopted for geometry parametrizations in CAD. (2005) as a numerical technique for the solution of partial differential equations. With the aim of a seamless integration with Computer-Aided Design, Isogeometric Analysis has been proposed by Hughes et al.
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