Helmholtz方程在多层无界声波导中特征问题计算

Eigenvalue computation in acoustic waveguides with some perfectly matched layers

尝试在深度方向引入PML(完美的匹配层)选取适当的非线性局部坐标正交变换及方程变换,将Helm-holtz方程uxx+uzz+k2(x,z)u=0变换为V■■+αV■■+βV■+γV=0,然后再选取非对称Rayleigh商迭代算法来求解Helmholtz方程的特征问题,即求解α2z+βz+γ的特征值和特征函数.数值模拟表明,此方法是可行的,并可以大大改善数值求解的效率.

The PML in transverse direction is inserted, a proper nonlinear local coordination and equation-transformation are chosen, and the Helmholtz equation uxx＋uzz＋k^2（x,z）u=0 into Vxx＋aVzz＋βVz＋rV=0 is changed, then the unsymmetric Rayleigh Quotient Iteration method is used to obtain the eigenvalue of the operator aδz^2＋βδz＋r. The result of numerical simulation indicates that this method is feasible and can improve the effciency of the numerical calculation.