Keynote Speaker:Chen Long

Abstract:

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 application of ODT.

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 ODT.

4. Quantization. Optimization algorithms based on ODT are applied to quantization to speed up the processing.

Introduction to the Speaker:

Chen Long is a professor at the University of California, Irvine currently. He graduated from Nanjing University with a bachelor's degree and Peking University with a master's degree. In 2005, he graduated with a Ph.D. from Pennsylvania State University, and his doctoral thesis won the Alumin Award from Pennsylvania State University. He has successively engaged in post-doctoral research at the University of California, San Diego and the University of Maryland. Since 2007, he has been working at the University of California, Irvine. His main research interests include the numerical methods of partial differential equations, the theory and application of adaptive finite element methods, the design and analysis of multi-grid methods, grid generation and computation geometry. Professor Chen Long has played a significant role in these fields, publishing over 60 papers inSIAM J Numer Anal,SIAM J Sci Comput,Math Computand other top journals of computational mathematics.

Inviter:

Rui Hongxing, Professor of School of Mathematics

Time:

11:00 on October 9 (Friday)

Location:

Tencent Meeting, ID: 855 328 567, password: 202010

Sponsored by: School of Mathematics, Shandong University