A Multilevel Method for Solving the Helmholtz Equation: The Analysis of the One-Dimensional Case

Abstract

In this paper we apply and discuss a multilevel method to solve a scattering problem. The multilevel method belongs to the class of incremental unknowns method as in [10]; in this work, the best performance was obtained with a coarsest grid having roughly two points per linear wavelength. We analyze this method for a simple model problem following H. Yserentant [17]. In this case, the main limitation to multilevel methods is closely linked to the indefiniteness of the Helmholtz problem.