Scientific Computing Group Seminars - Detail View

Speaker: G. Baruch

Affiliation: Tel Aviv University

Talk Title: Numerical Solution of Nonlinear Helmholtz Equations

Invited by: Chi-Wang Shu

Time: Nov. 06 2009 11 a.m.

Location: 182 George Street, Room 110

Abstract:

The nonlinear Helmholtz equation models the propagation of intense laser beams in Kerr media such as water, silica and air. It is a semilinear elliptic equation which requires non-selfadjoint radiation boundary-conditions, and remains unsolved in many configurations. We therefore consider the question, which has been open since the 1960s: do nonlinear Helmholtz solutions exist, under conditions for which the NLS solution becomes singular ? In other words, is the singularity removed in the elliptic model ? In this work we develop a numerical method which produces such solutions in some cases. We also consider the case of grated material, that has material discontinuities in the direction of propagation. We use a high-order finite-difference discretization which is compact only in the direction of propagation, that is optimal for this case. Joint work with Gadi Fibich and Semyon Tsynkov.