Analysis and application of two novel finite element methods for solving ziolkowski's pml model in the integro-differential form

Since the introduction of the perfectly matched layer (PML) technique by Be'\renger [J. P. Be'\renger, J. Comput. Phys., 114 (1994), pp. 185--200] to solve the time-dependent Maxwell's equations in unbounded domains, many different PML models have been developed and adopted for various wave propagation problems in unbounded domains. In this paper, we are interested in a physically inspired PML model proposed by Ziolkowski [R. W. Ziolkowski, Comput. Methods Appl. Mech. Engrg., 169 (1999), pp. 237--262]. To reduce the unknowns and make more efficient numerical methods, we reformulate the original model in integro-differential form. We propose and analyze two novel finite element methods for solving this equivalent PML model. Stability and convergence analysis are established for both schemes. Numerical results are presented to support our analysis and demonstrate the effectiveness of wave absorption of this equivalent PML.