Prof. Jichun Li

Center for Applied Mathematics and Statistics

Nevada Las Vegas (UNLV), USA

Speech Title: Two new finite element schemes for a time-domain carpet cloak model with metamaterials

Abstract

This talk is concerned about a time-domain carpet cloak model, which was originally derived in our previous work (Li et al., SIAM J. Appl. Math., 74(4), pp.1136–1151, 2014). The stability of a proposed explicit finite element scheme there is obtained under a quite restricted time step constraint $\tau=O(h^2)$. To overcome this disadvantage, here we propose two new finite element schemes for solving this carpet cloak model: one is the implicit Crank-Nicolson (CN) scheme, and another one is the explicit leap-frog (LF) scheme. By introducing a totally new energy different from the previous work, we manage to prove the unconditional stability for the CN scheme and conditional stability for the LF scheme under the practical CFL constraint $\tau=O(h)$. Optimal error estimates are also established for both schemes. Finally, numerical results are presented to support our analysis and demonstrate the cloaking phenomenon.

Biography

Jichun Li is Professor of Mathematics and Director for Center for Applied Mathematics and Statistics at University of Nevada Las Vegas (UNLV). He got his BS from Nanjing University and PhD from Florida State University. His previous positions include Postdoc Fellow at University of Texas at Austin and Associate Director of Institute for Pure and Applied Mathematics (IPAM) at UCLA.  He has published over 140 SCI journal papers and 2 monographs (one in the famous Springer Series in Computational Mathematics, vol.43, 2013). Currently, he serves as Editor-in-Chief of "Results in Applied Mathematics", and Managing Editor of "Computers & Mathematics with Applications" (both published by Elsevier).