Abstract
In this paper, we first give a quick review of the current status of the invisibility cloak with metamaterials. Then we focus on the carpet cloak model and establish an elegant stability different from our previous work. A similar discrete stability is also proved for a new FETD scheme. Then we prove the optimal convergence for this new scheme. Finally, we implement a new discontinuous Galerkin method and demonstrate its effectiveness in simulating the carpet cloaking phenomena.
Funding source: National Science Foundation
Award Identifier / Grant number: DMS-1416742
Funding source: National Natural Science Foundation of China
Award Identifier / Grant number: 11671340
Award Identifier / Grant number: 91430213
Funding statement: The first author was supported by NSF grant DMS-1416742 and NSFC project 11671340. The third author was supported by NSFC Key Project 91430213.
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