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 -

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.