Section:
New Results
Hermite type spline spaces over rectangular meshes with complex topological structures
Participants :
André Galligo, Bernard Mourrain.
Motivated by the Magneto HydroDynamic (MHD) simulation for Tokamaks
with Isogeometric analysis, we present in [14] a new type of splines defined over a rectangular mesh with arbitrary topology, which are piecewise
polynomial functions of bidegree and parameter
continuity. In particular, we compute their dimension and exhibit
basis functions called Hermite bases for bicubic spline spaces. We
investigate their potential applications for solving partial
differential equations (PDEs) over a complex physical domain in the
framework of Isogeometric analysis. In particular, we analyze the
property of approximation of these spline spaces for the
-norm. Despite the fact that the basis functions are singular at
extraordinary vertices, we show that the optimal approximation order
and numerical convergence rates are reached by setting a proper
parameterization.
This is a joint work with Meng Wu, Bernard Mourrain, André Galligo, Boniface Nkonga