| The perfectly matched layer(PML) is widely used for truncating unbounded domains in the calculation of waveguide [1,11,12]. How to select the optimal PML becomes a research hotspot. In this paper,we study the optimal parameters of PML based on a finite-difference approximation of Helmholtz equation. In essence,this problem is to select parameters of absorption function σ(x). The main measure is the average of reflection coefficients’model when the domain combines with a perfectly matched layer. The smaller numerical is,the better the results.Given an angle θ (Let θ be the angle between the z axis and wave vector).we can calculate a discrete reflection coefficient|Rθ|. In order to measure the optimal design of PML more coniprehensively.we present a definition of the discrete reflection coefficients’model|R|.Based on|R|,we study the selection of parameters for three kinds of absorp-tion function:1)c·tp;2)c·t3/1+t2;3)c1·t3/1+ce-t2.In the first category,we get the table of the optimal parameters. Accord-ing to the table and the practical situation,we can design the best absorption function.At the same time,this section also studies the related quantity. In the second category.|R|achieves the minimum0.0452when c=17. Compared with the first category.we can find that result is very close to the situation when p=1. Based on the first and the second category.we design the third kind of absorption function. In this category.we calculate the special case c1=1,and we get the result that|R|achieves the minimum0.05789while the only parameter is equal to21.4. Compared with the second category.we can find that results are almost the same. Then we consider the general situation that c1≠1. The results show that|R|achieves the minimum0.012763510when c1=1110.5and C2=0.061. This result is very close to the absorption function when p=3and s=83.3in the first category. It’s nearly four times better than the second category. It’s best. |
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