High-frequency numerical-analytic approximations for the separable acoustic wave equation
A joint numeric-asymptotic (WKB) approach in high frequency range is proposed for solving the separable wave equation in the context of underwater acoustic propagation. The concept of WKB is to use analytical asymptotic approximations (as in physical optics) to get the eigenvalues and eigenfunctions of Helmholtz equation under given boundary conditions wherever they are valid approximations. The numeric approach is limited to be used in the neighborhoods of turning points of the index of refraction profile. Error criteria for switch between methods are derived. The advantage of this WKB method is reducing of computing time by over an order of magnitude than conventional numeric method in that frequency range.
neighborhoods of turning points of the index of refraction profile
scientific article; zbMATH DE number 3961240
scientific article