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THB-splines: an effective mathematical technology for adaptive refinement in geometric design and isogeometric analysis. (English) Zbl 1425.65026

Summary: 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.

MSC:

65D07 Numerical computation using splines
65D17 Computer-aided design (modeling of curves and surfaces)

Software:

ISOGAT; G+Smo
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References:

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