一类带不平坦界面声波导中的共轭特征算子构造

Construction of adjoint eigenoperator for a class of acoustical waveguides with a curved interface.

无界且带有不平坦界面的声波导经坐标变换和完美匹配层截断,波的传播计算问题近似转化为在有界且带有平坦界面的声波导中数值求解改进Helmholtz方程,由于用步进算法解此改进复Helmholtz方程所涉及到的算子的特征函数一般不具有正交性,故在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;另一方面,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.

The unbounded acoustical waveguide with a curved interface is changed by the coordinate transformation and terminated by the perfectly matched layer. And the computation problem is approximately turned to the numerical solution of the improved Helmholtz equation on the bounded waveguide with a flatted interface. Since there is no orthogonal property of the eigenfunctions for the operator arising from the improved and complex Helmholtz equation fICHE）, it is very difficult to compute the coordinates under the local bases when the equation is solved by some numerical marching methods. In this paper, the equation of the adjoint eigenfunctions for ICHE is deduced, and it is proven that there is the orthogonal property between the eigenfunctions and the adjoint eigenfunctions. 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 use of the marching methods. Simulation numerical results show that the treatment is more feasible and effective.