Adaptive CAD model (re-)construction with THB-splines

Computer Aided Geometric Design

Sestini

2017

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We introduce an adaptive scattered data fitting scheme as extension of local least squares approximations to hierarchical spline spaces. To efficiently deal with non-trivial data configurations, the local solutions are described in terms of (variable degree) polynomial approximations according not only to the number of data points locally available, but also to the smallest singular value of the local collocation matrices. These local approximations are subsequently combined without the need of additional computations with the construction of hierarchical quasi-interpolants described in terms of truncated hierarchical B-splines. A selection of numerical experiments shows the effectivity of our approach for the approximation of real scattered data sets describing different terrain configurations.

Section: Related Workmentioning

confidence: 99%

Adaptive scattered data fitting by extension of local approximations to hierarchical splines

Bracco

Computer Aided Geometric Design

Sestini

2017

Self Cite

“…Based on the multi-level concept of HB-splines, truncated hierarchical B-splines (THB-splines) [12], have also been proposed as an effective tool to perform hierarchical refinement while reducing the interactions between different levels in the spline hierarchy. The truncated basis has been successfully applied in different problems related to computer aided design [13,14] and isogeometric analysis [15,16,17]. It is worth to mention that, while several papers investigated refinement schemes for adaptive isogeometric methods in the last years, only very recently, few authors also focused on the study of suitable and effective mesh coarsening [18,19].…”

Section: Introductionmentioning

confidence: 99%

Suitably graded THB-spline refinement and coarsening: Towards an adaptive isogeometric analysis of additive manufacturing processes

Carraturo

Computer Methods in Applied Mechanics and Engineering

Reali

et al. 2019

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In the present work we introduce a complete set of algorithms to efficiently perform adaptive refinement and coarsening by exploiting truncated hierarchical B-splines (THB-splines) defined on suitably graded isogeometric meshes, that are called admissible mesh configurations. We apply the proposed algorithms to two-dimensional linear heat transfer problems with localized moving heat source, as simplified models for additive manufacturing applications. We first verify the accuracy of the admissible adaptive scheme with respect to an overkilled solution, for then comparing our results with similar schemes which consider different refinement and coarsening algorithms, with or without taking into account grading parameters. This study shows that the THB-spline admissible solution delivers an optimal discretization for what concerns not only the accuracy of the approximation, but also the (reduced) number of degrees of freedom per time step. In the last example we investigate the capability of the algorithms to approximate the thermal history of the problem for a more complicated source path. The comparison with uniform and non-admissible hierarchical meshes demonstrates that also in this case our adaptive scheme returns the desired accuracy while strongly improving the computational efficiency.

“…For this reason, a new hierarchical basis -the truncated basis for hierarchical splines (THB-splines) -has recently been introduced [18]. THB-splines, defined as suitable linear combinations of refined B-splines, form a convex partition of unity, exhibit good stability and approximation properties [17,42], and are suitable for applications in computer aided design [28]. By providing a way to define an adaptive extension of the B-spline framework which is also suitable for geometric modeling applications, THB-splines satisfy both the demands of adaptive numerical simulation and geometric design, making them well suited for isogeometric analysis.…”

Section: Introductionmentioning

confidence: 99%

THB-splines: An effective mathematical technology for adaptive refinement in geometric design and isogeometric analysis

Computer Methods in Applied Mechanics and Engineering

Jüttler

Kleiss

et al. 2016

Self Cite

124

Local refinement with hierarchical B-spline structures is an active topic of research in the context of geometric modeling and isogeometric analysis. By exploiting a multilevel control structure, we show that truncated hierarchical B-spline (THB-spline) representations support interactive modeling tools, while simultaneously providing effective approximation schemes for the manipulation of complex data sets and the solution of partial differential equations via isogeometric analysis. A selection of illustrative 2D and 3D numerical examples demonstrates the potential of the hierarchical framework.