TY - JOUR
T1 - Quadratic splines on quad-tri meshes
T2 - Construction and an application to simulations on watertight reconstructions of trimmed surfaces
AU - Toshniwal, Deepesh
PY - 2022
Y1 - 2022
N2 - 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. Furthermore, the refinement process leaves the splines invariant on the mesh boundary. Numerical tests indicate that the spline spaces demonstrate optimal approximation behaviour in the L2 and H1 norms under mesh refinement, and provide a viable approach to simulations on watertight reconstructions of trimmed surfaces.
AB - 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. Furthermore, the refinement process leaves the splines invariant on the mesh boundary. Numerical tests indicate that the spline spaces demonstrate optimal approximation behaviour in the L2 and H1 norms under mesh refinement, and provide a viable approach to simulations on watertight reconstructions of trimmed surfaces.
KW - Analysis-suitable splines
KW - Isogeometric analysis
KW - Optimal approximation
KW - Quadrilateral-triangle meshes
KW - Trimmed surfaces
UR - http://www.scopus.com/inward/record.url?scp=85117209865&partnerID=8YFLogxK
U2 - 10.1016/j.cma.2021.114174
DO - 10.1016/j.cma.2021.114174
M3 - Article
AN - SCOPUS:85117209865
VL - 388
SP - 1
EP - 29
JO - Computer Methods in Applied Mechanics and Engineering
JF - Computer Methods in Applied Mechanics and Engineering
SN - 0045-7825
M1 - 114174
ER -