报 告 人: 蔡伟 教授 (美国北卡大学夏洛特分校和上海交通大学)

报告时间: 2014年6月 16日（周一）13:30～15:00

报告地点: 校本部东区计算机大楼1104室

邀 请 人: 张武 教授

Abstract：
In this talk, we will introduce two new ideas how to achieve adaptivity in numerical methods for modeling electric many body effects in two problems. The first problem is how to treat the Poisson-Boltzmann electrostatics using a combined atomistic and continuum electrostatic hybrid model in protein folding and ion-channel transport. The idea is to partition the simulation system into two regions: one explicit region in regular simple geometry shapes (spheres or cylinders) where solute/ion channel protein plus nearby solvent molecules are described in atomistic details while the exterior of the explicit region will be described by continuum electrostatics. The polarization of the continuum media (solvent or membrane) will be efficiently represented by newly developed image methods and the dynamics of the particles in the explicit region will be computed by molecular dynamics with FMM for acceleration of Coulombic interactions. In the second problem of finding linear scaling DFT solver for ground state energies of many electron systems, we extend the popular discontinuous Galerkin (DG) approach in CFD and CEM to the density matrix minimization for the ground state energy. Due to the flexibility in the construction of DG finite element basis, it is straightforward to introduce physics based local orbitals (using the local nucleus potential) into the traditional polynomial finite element spaces. As such, the number of the unknowns in the support functions used for the sparse representation of the density matrix can be reduced to a minimum as the local physics orbital capture the main behavior of the electron wave functions. We will present numerical results for the ion-solvation in ionic solvent in the first problem and the linear scaling performance of the DG-DFT solver for a model quantum system.

Biography：
Dr. Cai got the Ph.D. degree in 1989 from Brown University. Since 1999, Dr. Cai has been a tenured full professor in mathematics at University of North Carolina at Charlotte. He also holds a Chair professor at the Institute of Natural Sciences at Shanghai Jiao Tong University and is a Shanghai 1000 talent award (class B) recipient. In 2005, he was awarded the Feng Kang Prize of scientific computing. His research has been supported recently by National Science Foundation, Department of Energy, Army Research Office, and National Institutes of Health and Chinese NSF. His research interest cover multiple research fields in scientific and engineering computing, in particular, in computational electromagnetics, electrostatic interactions in computational biology, and quantum device transport, and combustions etc. He published 90+ papers in peer-reviewed international journals and is the author of the book "Computational Methods for Electromagnetic Phenomena: electrostatics in solvation, scattering and electron transport" published by Cambridge University Press, 2013, 461 pages.