Two absorbing boundary conditions (ABC's) are derived for the cylindrical MRTD grids. The first one is the convolutional perfectly matched layer (CPML) based on stretched coordinates with complex frequency shifted constitutive parameters, and the other is the straightforward extension of CPML named quasi-CPML (QCPML) as it is no longer perfectly matched for cylindrical interfaces. Unlike the Berenger's PML, the implementations of the two ABC's are completely independent of the host material. Numerical results show that both ABC's can provide a quite satisfactory absorbing boundary condition, and can save more CPU time and memory than the Berenger's PML, while the QCPML has an advantage of CPML at the proposed absorbing performance, CPU time and memory saving. Moreover, it is shown that the QCPML is more effective than the PML and CPML at absorbing evanescent waves.
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