Now showing items 1-4 of 4
Gaussian quadrature for $C^1$ cubic Clough-Tocher macro-triangles
A numerical integration rule for multivariate cubic polynomials over n-dimensional simplices was designed by Hammer and Stroud . The quadrature rule requires n + 2 quadrature points: the barycentre of the simplex and ...
Efficient quadrature rules for subdivision surfaces in isogeometric analysis
We introduce a new approach to numerical quadrature on geometries defined by subdivision surfaces based on quad meshes in the context of isogeometric analysis. Starting with a sparse control mesh, the subdivision process ...
On numerical quadrature for $C^1$ quadratic Powell-Sabin 6-split macro-triangles
The quadrature rule of Hammer and Stroud  for cubic polynomials has been shown to be exact for a larger space of functions, namely the $C^1$ cubic Clough-Tocher spline space over a macro-triangle if and only if the ...
Towards optimal advection using stretch-maximizing stream surfaces
We investigate a class of stream surfaces that expand in time as much as possible. Given a vector field, we look for seed curves that locally propagate in time in a stretch-maximizing manner, i.e., curves that infinitesimally ...