| Finite difference time domain (FDTD) method has been developed rapidiy in recent years and widely applied. In FDTD method, the Maxwell curl equations are changed into the difference equations by using the Yee Cell as the discrete units, and the presence of it can handle very complex electromagnetic problems combining with computer technology, so it becomes more important in engineering electromagnetic fields.In FDTD method the limited grid space is used to simulate that the electromagnetic wave propagation in unbounded space, so the boundary must be truncated to implement a particular algorithm.This algorithm must be implemented in the limited grid space, and also, be able to minimize the wave reflection on the boundary, and be improved accuracy. This special algorithm which effect on the truncation boundary can be called as the absorbing boundary conditions (ABC) generally.Firstly, this paper introduces the ABCs' development, and then do some in-depth research about the nearly perfectly matched layer (NPML) proposed by Professor Cummer. In this paper, I can start it from two ways mainly:1) Using this method in truncating the normal medium. In this way, the NPML method avoids the field-splitting, and combine with the examples to show it's rationality, and take the results to compare with other numerical methods, then, analysis its feasibility.2) By using this method to truncate the dispersive media, and the modified NPML (M-NPML) method is presented. This method makes some variables in Maxwell's equations which partial derivative of the space to stretching the coordinate .And it does not require to introduct the other additional variables to the auxiliary equation ,and makes the auxiliary equation has the same iterative in the normal medium with the dispersive media. This method used here is simple in presentation and easy to understand, and makes the programming more easier, reduces the complexity. Compared with the UPML method ,this method is more simpler.
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