FINITE DIFFERENCE METHODS FOR THE NONLINEAR EQUATIONS OF PERTURBED GEOMETRICAL OPTICS

Abstract

Finite difference methods are developed to solve the nonlinear partial differential equations approximating solutions of the Helmholtz equation in high frequency regime. Numerical methods are developed for solving the geometrical optics approximation, the classical asymptotic expansion, and a new perturbed geometrical optics system. We propose a perturbed geometrical optics system to recover diffraction phenomena that are lost in geometrical optics approximations. We discuss techniques we have developed for recovering multivalued solutions and we present numerical examples computed with finite difference approximations of the above systems. [Vol. 11, No. 1 (1996), pp 90-98, Special issue on Applied Mathematics: Meeting the challenges presented by computational electromagnetics]