TY - JOUR
T1 - Hermite Type Spline Spaces over Rectangular Meshes with Complex Topological Structures
AU - Wu , Meng
AU - Mourrain , Bernard
AU - Galligo , André
AU - Nkonga , Boniface
JO - Communications in Computational Physics
VL - 3
SP - 835
EP - 866
PY - 2018
DA - 2018/04
SN - 21
DO - http://doi.org/10.4208/cicp.OA-2016-0030
UR - https://global-sci.org/intro/article_detail/cicp/11262.html
KW - 
AB - <p style="text-align: justify;">Motivated by the magneto hydrodynamic (MHD) simulation for Tokamaks
with Isogeometric analysis, we present splines defined over a rectangular mesh with a
complex topological structure, i.e., with extraordinary vertices. These splines are piecewise
polynomial functions of bi-degree (d,d) and $C^r$ parameter continuity. And 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 physical domain in the framework of Isogeometric analysis.
For instance, we analyze the property of approximation of these spline spaces for the $L^2$-norm; we show that the optimal approximation order and numerical convergence
rates are reached by setting a proper parameterization, although the fact that the basis
functions are singular at extraordinary vertices.</p>