TY - JOUR T1 - A Multilevel Method for Solving the Helmholtz Equation: The Analysis of the One-Dimensional Case JO - International Journal of Numerical Analysis and Modeling VL - 3 SP - 365 EP - 372 PY - 2011 DA - 2011/08 SN - 8 DO - http://doi.org/ UR - https://global-sci.org/intro/article_detail/ijnam/690.html KW - hierarchical basis, indefinite problem, Helmholtz equation, iterative methods. AB -

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.