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The original Bérenger’s perfectly matched layer (PML) was quite effective in simulating wave propagation problem in unbounded domains. But its stability is very challenging to prove. Later, some equivalent PML models were developed by Bécache and Joly [ ESAIM: M2AN 36 (2002) 87–119] and their stabilities were established. Hence studying and developing efficicent numerical methods for solving those equivalent PML models are needed and interesting. Here we propose a novel explicit unconditionally stable finite element scheme to solve an equivalent Bérenger’s PML model. Both the stability and convergence analysis are proved for the proposed scheme. Numerical results justifying the theoretical analysis are presented. We also demonstrate the effectiveness of this PML in simulating wave propagation in the free space. To our best knowledge, this is the first explicit unconditionally stable finite element scheme developed for this PML model. 

Abstract In this paper, we develop a local discontinuous Galerkin (LDG) method to simulate the wave propagation in an electromagnetic concentrator. The concentrator model consists of a coupled system of four partial differential equations and one ordinary differential equation. Discrete stability and error estimate are proved for both semi‐discrete and full‐discrete LDG schemes. Numerical results are presented to justify the theoretical analysis and demonstrate the interesting wave concentration property by the electromagnetic concentrator.