Isogeometric Analysis on surfaces with arbitrary topology

报告时间：2017年4月14日（星期五）15:00-16:00

报告地点：数学学院509

报告人：Bernard Mourrain

工作单位：法国国家信息与自动化研究所（INRIA）

举办单位：数学学院

报告人简介：

法国国家信息与自动化研究所Bernard MOURRAIN教授长期从事在几何造型、计算机辅助几何、计算符号代数等方向的研究。计算数学领域Journal of Symbolic Computation、SIAM Journal on Applied Algebra and Geometry编委成员、计算几何领Theoretical Computer Science, Computer Aided Geometric Design等受邀编辑。多个计算几何领域国际核心期刊，如Applicable Algebra in Engineering Communication and Computing, Discrete Applied Mathematics, Theoretical Computer Science, Computer Aided Geometric Design, Computer Aided Design, Math. Of Comp, Math, Review, CRAS的评审人以及ISSAC、Geometric Modeling and Processing、Symposium on Solid and Physical Modeling, Symbolic-Numeric Computation, MEGA, ACA, ADG, ACSM等计算几何与符号计算国际会议Program chair, program co-chair以及Member of program committees。

报告内容：

In Isogeometric Analysis, the same spline function space is used to describe the geometry of the computational domain and an approximation of the solutions of PDE equations. Obstacle occurs in this methodology when the computation domain has a complex topology, so that classical b-spline basis functions cannot be employed.

We describe geometrically continuous splines, which allow to handle computational domains with arbitrary topology and show how they can be used in the Isogeometric framework.

We analyze the space of piecewise polynomial differentiable functions on a mesh of general topology. This linear space of spline functions is characterized by glueing data across the shared edges. Using algebraic techniques, which involve the analysis of the module of syzygies of the glueing data, we give dimension formula for the space of geometrically smooth splines of degree k, for arbitrary topology when k is big enough. We provide explicit constructions of basis functions attached respectively to vertices, edges and faces.