偏微分方程和计算数学学术报告
报告人： 张 镭博士
时 间： 2011年8月31日（星期三）上午：10:00-11:00
地 点： 中山北路校区理科大楼A座1510室
报告题目： Homogenization with non-separable scales
报告摘要：
We consider homogenization of divergence form operators with $L^\infty$
coefficients which allows non-separable scales, in the sense that the solution space is approximated with a finite dimensional space.
Our method does not rely on concepts of ergodicity or scale-separation, but on the property that the solution space of these operators is
compactly embedded in $H1$ if source terms are in the unit ball of $L2$
instead of the unit ball of $H^{-1}$. Approximation spaces are generated
by solving elliptic PDEs on localized sub-domains with source terms
corresponding to approximation bases for $H2$. The $H1$-error estimates
show that $\mathcal{O}(h^{-d})$-dimensional spaces with basis elements
localized to sub-domains of diameter $\mathcal{O(h^\alpha
\ln\frac{1}{h})$ (with $\alpha \in [1/2,1)$) result in an
$\mathcal{O}(h^{2-2\alpha})$ accuracy for elliptic, parabolic and
hyperbolic problems. The proposed method can be naturally generalized to
vectorial equations (such as elasto-dynamics).

报告人简介：
主要教育学历
Ph.D., 2007, California Institute of Technology, Pasadena
Advisor: Professor Houman Owhadi

Thesis: Metric based upscaling for partial differential equations

M.S., 2002, Chinese Academy of Sciences, Beijing

Advisor: Professor Li Yuan

Thesis: Level set method for two component compressible ow simulation.

B.S., 1999, Peking University, Beijing, China.

主要研究经历

Jun.2010 - Jun,2012, Research Associate, Mathematical Institute, Oxford University

Apr.2009 - May.2010, Postdoc scholar, Hausdor Center for Mathematics, Bonn, Germany

Sep.2007 - Mar.2009, Postdoc scholar, Max Planck Institute for mathematics in sciences, Leipzig, Germany.

研究方向
Research: Multiscale analysis and modeling in science and engineering

Interest: Numerical analysis and scientific computing, Homogenization of partial differential equations,

Quasi-continuum method and its application in material science