修正的卷积完全匹配层技术

Modified convolutional perfectly matched layer technique

复频移的卷积完全匹配层(convolutional perfectly matched layer,CPML)与时域有限差分(finitedifference time-domain,FDTD)算法递推公式之间存在数值计算时间不同步的问题,诸多算例结果表明CPML的吸波效果并没有达到一些具有相同二阶精度的完全匹配层(perfectly matched layer,PML)的吸波效果。文章采用时间平均近似方法对CPML进行了修正,使其吸波性能与其他具有相同数值计算精度的PML的吸波性能相当;通过2个具有代表性的算例,验证了方法的有效性。该方法思路简单、清晰,只需在传统的CPML代码基础上进行简单的修改,计算时间大大缩减,该方法对于CPML在FDTD算法中的高效应用具有一定的意义。

The numerical computation time is not consistent between the complex frequency-shifted convolutional perfectly matched layer(CPML)and the recursive formula of the finite-difference timedomain(FDTD)method.It is found that the absorption effect of CPML does not reach the absorption effect of some perfectly matched layers(PMLs)with the same second-order accuracy in many numerical examples.In this paper,the time average approximation method is applied to modifying the traditional CPML,making sure that its absorption effect nearly has the same performance with other PMLs which have the same numerical accuracy.The validity of this method is verified by two representative examples.The presented method based on the simple modification to the traditional CPML code can greatly reduce the computation time,which is of significance for the efficient application of CPML in the FDTD algorithm.