2022 2nd International Conference on Statistics, Applied Mathematics and Computing Science(CSAMCS 2022)
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Prof. Jichun Li

Prof. Jichun Li

Center for Applied Mathematics and Statistics

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.