Research on the convolutional PML absorbing boundary conditions for the FDTD method

The convolutional perfectly match layer (CPML) is a kind of widely-used absorbing boundary conditions (ABCs) for the finite-difference time domain (FDTD) method, but its complexity and intricacy makes it very difficult to be coded. Some easy-made mistakes such as incorrectly dealing with edges and angular points of CPML media, wrongly determining the coefficients of convolutional terms, etc., are introduced. In addition, a modified formula about CPML is proposed, which can improve its absorption performance greatly. A numerical experiment is presented to illustrate how to code the program correctly, Meanwhile, the calculation results show that the modified formula is more accurate in comparison with the conventional one.