Efficient Multigrid and Data Structures for Edge-Oriented FEM Stabilization

Abstract

We study edge-oriented FEM stabilizations w.r.t. linear multigridsolvers and data structures with the goal to examine the efficiencyof such stabilizations due to the extending matrix stencil whichis not supported by standard FEM data structures. A new edge-orienteddata structure has been developed to support the additional coupling.So, the local element-wise and edge-wise matrices are easily deducedfrom the global ones. Accordingly, efficient Vanka smoothers areintroduced, namely a full cell-oriented and an edge-oriented Vankasmoother so that it becomes possible to privilege edge-oriented stabilizationfor CFD simulations.