#5599. Quadratic splines on quad-tri meshes: Construction and an application to simulations on watertight reconstructions of trimmed surfaces

August 2026publication date
Proposal available till 21-05-2025
4 total number of authors per manuscript0 $

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Journal’s subject area:
Computational Mechanics;
Mechanical Engineering;
Mechanics of Materials;
Physics and Astronomy (all);
Computer Science Applications;
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Abstract:
Given an unstructured mesh consisting of quadrilaterals and triangles (we allow both planar and non-planar meshes of arbitrary topology), we present the construction of quadratic splines of mixed smoothness — C1 smooth away from the unstructured regions of T and C0 smooth otherwise. The splines have several useful B-spline-like properties – partition of unity, non-negativity, local support and linear independence – and allow for straightforward imposition of boundary conditions. We propose a non-nested refinement process for the splines with multiple advantages — a simple computer implementation, reduction in the footprint of C0 smoothness, boundary preservation, and excellent approximation behaviour in simulations.
Keywords:
Analysis-suitable splines; Isogeometric analysis; Optimal approximation; Quadrilateral-triangle meshes; Trimmed surfaces

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