报告时间：2016年7月21日(星期四)，下午14：30
报告地点：紫金港校区蒙民伟楼422会议室
报告题目：Isogeometric Analysis on Triangulation
报告人：Dr. Xiaoping Qian
主持人：高曙明 教授
Abstract:Isogeometric analysis is a numerical analysis technique that uses basis functions commonly found in CAD geometries to represent both geometry and to approximate the solutions of problems governed by partial differential equations (PDE). It alleviates the burden of model conversion and approximation in analysis. The increased continuity of the basis has significant numerical advantages over traditional finite element analysis, e.g. improved convergence rate on a per degree-of-freedom basis.
In this talk, I will present a method for isogeometric analysis on the triangulation of a domain bounded by non-uniform rational B-splines (NURBS) curves/surfaces. In this method, both the geometry and the physical field are represented by bivariate/trivariate splines in Bernstein–Bézier form over the triangulation. We describe a set of procedures to construct a parametric domain and its triangulation from a given physical domain, construct Cr-smooth basis functions over the domain, and establish a rational Triangular Bézier Spline (rTBS) based geometric mapping that Cr-smoothly maps the parametric domain to the physical domain and exactly recovers the NURBS boundaries at the domain boundary. As a result, this approach can achieve automated meshing of objects with complex topologies and allow highly localized refinement. Isogeometric analysis of problems from linear elasticity and advection–diffusion analysis is demonstrated. Numerical examples demonstrate that our method achieves optimal convergence and can handle complex geometries.
Bio: Dr. Xiaoping Qian is an Associate Professor in the Department of Mechanical Engineering at the University of Wisconsin, Madison. He obtained his Ph.D. in Mechanical Engineering from the University of Michigan, Ann Arbor. His research interests lie in geometric modeling and optimization and their applications in design and manufacturing. His research activities have been supported by various grants from NSF, AFOSR and others. He has received multiple best papers awards from ASME and the Solid Modeling Association. He is an Associate Editor of the ASME Journal of Computing and Information Science in Engineering, ASME Journal of Manufacturing Science and Engineering, and he is on the editorial board of the journal Computer-Aided Design and the Chinese journal CAD &CG.
