一类带PML声波导中的共轭特征函数构造及其应用

Construction of conjugate eigenfunctions and its application for a class of acoustical waveguides with PML

在带有完美匹配层的有界区域中,由于改进的复Helmholtz方程的特征函数一般不具有正交性,故数值步进求解复方程时存在着局部基下坐标计算的困难.本文一方面推导出此复偏微分方程的共轭特征函数所满足的方程,并论证方程的特征函数与共轭特征函数正交之性质;另一面,给出局部基下坐标计算的简便公式,它可使步进计算保持高效率.数值模拟结果表明所提方法切实可行、有效.

In the bounded region with the perfectly matched layer, since there is no orthogonal property of the eigen- functions for the improved and complex Helmholtz equation （ICHE）, it is difficult to compute the coordinates under the local bases when the equation is solved by some numerical marching methods. The equation of the conjugate ei- genfunctions for ICHE is deduced, and it is proven that there is the orthogonal property between the eigenfunctions and the conjugate functions. On the other hand, a simple and convenient formula is given to calculate the coordinates under the local bases. This may ensure the higher efficiency by using the marching methods. Numerical simulation results show that the treatment is more feasible and efficient.