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Maseeh Colloquium: Optimal Delaunay Triangulations
Friday, October 4, 2013 - 3:15pm

The Maseeh Mathematics and Statistics Colloquium Series* presents

Optimal Delaunay Triangulations
by Long Chen, Ph.D., University of California at Irvine

Friday, October 4th, 2013 at 3:15pm 
Neuberger Hall room 454 | Portland State University
(Refreshments served at 3:00 in presentation room)
This event is free and open to the public. 

Optimal Delaunay triangulations (ODTs) are optimal meshes minimizing the interpolation error to a convex function in Lp norm. In this talk we shall present several applications of ODTs. 

  1. Mesh smoothing. Meshes with high quality are obtained by minimizing the interpolation error in a weighted L1 norm. 
  2. Anisotropic mesh adaptation. Optimal anisotropic interpolation error estimate is obtained by choosing anisotropic functions. The error estimate is used to produce anisotropic mesh adaptation for convection-dominated problems. 
  3. Sphere covering and convex polytope approximation. Asymptotic exact and sharp estimate of some constant in these two problems are obtained from ODTs. 
  4. Quantization. Optimization algorithms based on ODTs are applied to quantization to speed up the processing.

About the Speaker:
Long Chen graduated from Pennsylvania State University 2005 and then spend one year in University of California at San Diego and one year in University of Maryland as postdocs. Since 2007, he joined University of California at Irvine as an Assistant Professor. In 2011, he got tenured and became Associated Professor. 

Chen's research interest includes computational geometry and numerical methods for solving partial differential equations. In particular he worked on mesh generation and optimization, adaptive finite element method, and multigrid methods. His research is constantly supported by NSF and partially supported by DOE.

* Sponsored by the Maseeh Mathematics and Statistics Colloquium Series Fund and the Fariborz Maseeh Department of Mathematics & Statistics, PSU.