1,198 research outputs found
Unstructured spline spaces for isogeometric analysis based on spline manifolds
Based on spline manifolds we introduce and study a mathematical framework for
analysis-suitable unstructured B-spline spaces. In this setting the parameter
domain has a manifold structure, which allows for the definition of function
spaces that have a tensor-product structure locally, but not globally. This
includes configurations such as B-splines over multi-patch domains with
extraordinary points, analysis-suitable unstructured T-splines, or more general
constructions. Within this framework, we generalize the concept of
dual-compatible B-splines, which was originally developed for structured
T-splines. This allows us to prove the key properties that are needed for
isogeometric analysis, such as linear independence and optimal approximation
properties for -refined meshes
Bivariate Hermite subdivision
A subdivision scheme for constructing smooth surfaces interpolating scattered data in is proposed. It is also possible to impose derivative constraints in these points. In the case of functional data, i.e., data are given in a properly triangulated set of points from which none of the pairs and with coincide, it is proved that the resulting surface (function) is . The method is based on the construction of a sequence of continuous splines of degree 3. Another subdivision method, based on constructing a sequence of splines of degree 5 which are once differentiable, yields a function which is if the data are not 'too irregular'. Finally the approximation properties of the methods are investigated
Almost- splines: Biquadratic splines on unstructured quadrilateral meshes and their application to fourth order problems
Isogeometric Analysis generalizes classical finite element analysis and
intends to integrate it with the field of Computer-Aided Design. A central
problem in achieving this objective is the reconstruction of analysis-suitable
models from Computer-Aided Design models, which is in general a non-trivial and
time-consuming task. In this article, we present a novel spline construction,
that enables model reconstruction as well as simulation of high-order PDEs on
the reconstructed models. The proposed almost- are biquadratic splines on
fully unstructured quadrilateral meshes (without restrictions on placements or
number of extraordinary vertices). They are smooth almost everywhere,
that is, at all vertices and across most edges, and in addition almost (i.e.
approximately) smooth across all other edges. Thus, the splines form
-nonconforming analysis-suitable discretization spaces. This is the
lowest-degree unstructured spline construction that can be used to solve
fourth-order problems. The associated spline basis is non-singular and has
several B-spline-like properties (e.g., partition of unity, non-negativity,
local support), the almost- splines are described in an explicit
B\'ezier-extraction-based framework that can be easily implemented. Numerical
tests suggest that the basis is well-conditioned and exhibits optimal
approximation behavior
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