Conjugate In A Class With A Flat Interface Acoustic Waveguide Operator Constructed

The unbounded acoustical waveguide with the curved interface is changed by the coordinate transform 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 improved and complex Helmholtz equation(ICHE),it is very difficult to compute the coordinates under the local baseswhen 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 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 use of the marching methods.Simulation numerical results show that the treatment is more feasible and efficient.