THE RICCATI METHOD FOR THE HELMHOLTZ-EQUATION

The operator Riccati equation for the Dirichlet-to-Neumann map is deri ved from the exact operator factorization of the two-dimensional varia ble coefficient Helmholtz equation. Numerical schemes are developed fo r the operator Riccati equation acid its variant using a local eigenfu nction expansion. This leads to a practical computational method for a coustic wave propagation over large range distances, since the boundar y value problem of the Helmholtz equation is reduced to ''initial'' va lue problems that are solved by marching in the range. The efficiency and accuracy of the method is demonstrated by numerical experiments in cluding the plane-parallel range-dependent waveguide benchmark problem proposed by the Acoustical Society of America. (C) 1996 Acoustical So ciety of America.