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- W3097603138 abstract "With the aim of a seamless integration with Computer-Aided Design, Isogeometric Analysis has been proposed by Hughes et al. (2005) as a numerical technique for the solution of partial differential equations. Indeed, isogeometric analysis is based on splines, the same functions that are adopted for geometry parametrizations in CAD. Smooth splines yield two important benefits when compared to C0 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. In this chapter we review three different methods to construct C1 isogeometric spaces on multi-patch domains or unstructured quadrilateral meshes. The first, proposed in Collin et al. (2016), is based on the concept of geometric continuity, well-known in geometric design. The second, from Toshniwal et al. (2017c), uses a specific singular construction (the D-patch construction) at extraordinary points. The third is a polar construction from Toshniwal et al. (2017a). Such constructions possess properties that make them suitable for performing both computational analysis and geometric modeling." @default.
- W3097603138 created "2020-11-09" @default.
- W3097603138 creator A5031451887 @default.
- W3097603138 creator A5059485119 @default.
- W3097603138 creator A5059966357 @default.
- W3097603138 creator A5063049746 @default.
- W3097603138 date "2021-01-01" @default.
- W3097603138 modified "2023-09-23" @default.
- W3097603138 title "Smooth multi-patch discretizations in Isogeometric Analysis" @default.
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