Efficient Implementation of Nonuniform Refinement Levels in a Geometric Multigrid Finite-Element Method for Electromagnetic Waves

We present an advanced geometric multigrid strategy for finite-element (FE) meshes of nonuniform refinement levels. The proposed method exploits the fact that levels of high resolution usually extend over small subdomains only. By restricting the smoothing operations at the finer levels to the corresponding partial meshes, both memory consumption and operation count are kept at a minimum. Our computer implementation is based on a hierarchy of perfectly nested FE spaces and employs hanging variables to interface between regions of unequal refinement levels. To validate the effectiveness of the suggested approach, several numerical examples are given