Research On The Conjugate Operator And Orthogonality Of Acoustic Waveguide Based On Perfect Matching Layer

Researchers usually set the artificial boundary by adding a perfectly matched layer when they truncate the unbounded region into a bounded region.Perfectly matched layer was proposed by Berenger in 1994,it can effectively absorb the waves spread from all angles and no sound reflection.The wave exponentially decays rapidly in the perfectly matched layer,the reflected waves are again ab-sorbed,and finally almost all are absorbed.The addition of perfectly matched layer makes the Helmholtz equation become a complex coefficient partial differ-ential equation,and the characteristic modes are no longer orthogonal,which brings the computational difficulties for the transformation of local basis.For a flat interface,this paper constructs its conjugate characteristic operator,and the-oretically derives its orthogonality.In ocean media,the bottom of the sea floor is usually a curved soil layer.Therefore,for the curved interface,the interface needs to be straightened first.In this paper,the local orthogonal transformation is used to transform the coordinates.Then we construct characteristic operator after transformation.In this paper,we chose some samples to verify the theory by numerical sim-ulation.Because of the existence of analytic solution,flat interface can directly calculate the cross integral of eigenfunction and conjugate eigenfunction.And we use adaptive Gaussian integration to improve the accuracy.Curved interface doesn't have the analytic solution,the use of finite difference method to obtain discrete eigenfunction.The experimental results verify the correctness of the cross-orthogonality.