
C^ssmooth isogeometric spline spaces over planar multipatch parameterizations
The design of globally C^ssmooth (s ≥ 1) isogeometric spline spaces ove...
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Isogeometric collocation on planar multipatch domains
We present an isogeometric framework based on collocation for solving th...
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C^1 isogeometric spline space for trilinearly parameterized multipatch volumes
We study the space of C^1 isogeometric spline functions defined on trili...
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An optimally convergent smooth blended Bspline construction for unstructured quadrilateral and hexahedral meshes
Easy to construct and optimally convergent generalisations of Bsplines ...
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TreeCotree Decomposition of Isogeometric Mortared Spaces in H(curl) on MultiPatch Domains
When applying isogeometric analysis to engineering problems, one often d...
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Computation of multidegree Tchebycheffian Bsplines
Multidegree Tchebycheffian splines are splines with pieces drawn from e...
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THUSplines: Highly Localized Refinement on Smooth Unstructured Splines
We present a novel method named truncated hierarchical unstructured spli...
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Construction of approximate C^1 bases for isogeometric analysis on twopatch domains
In this paper, we develop and study approximately smooth basis constructions for isogeometric analysis over twopatch domains. One key element of isogeometric analysis is that it allows high order smoothness within one patch. However, for representing complex geometries, a multipatch construction is needed. In this case, a C^0smooth basis is easy to obtain, whereas C^1smooth isogeometric functions require a special construction. Such spaces are of interest when solving numerically fourthorder PDE problems, such as the biharmonic equation and the KirchhoffLove plate or shell formulation, using an isogeometric Galerkin method. With the construction of socalled analysissuitable G^1 (in short, ASG^1) parametrizations, as introduced in (Collin, Sangalli, Takacs; CAGD, 2016), it is possible to construct C^1 isogeometric spaces which possess optimal approximation properties. These geometries need to satisfy certain constraints along the interfaces and additionally require that the regularity r and degree p of the underlying spline space satisfy 1 ≤ r ≤ p2. The problem is that most complex geometries are not ASG^1 geometries. Therefore, we define basis functions for isogeometric spaces by enforcing approximate C^1 conditions following the basis construction from (Kapl, Sangalli, Takacs; CAGD, 2017). For this reason, the defined function spaces are not exactly C^1 but only approximately. We study the convergence behavior and define function spaces that converge optimally under hrefinement, by locally introducing functions of higher polynomial degree and lower regularity. The convergence rate is optimal in several numerical tests performed on domains with nontrivial interfaces. While an extension to more general multipatch domains is possible, we restrict ourselves to the twopatch case and focus on the construction over a single interface.
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