High Performance FEM Simulation in CFD and CSM

Processor technology is still dramatically advancing and promises further enormous improvements in processing data for the next decade. In contrast, much lower advances in moving data are expected such that the efficiency of many numerical software tools for Partial Differential Equations (PDEs) is restricted by the cost for memory access. In last year’s Research Report [7] we outlined the numerical concepts pursued at our chair to overcome the pinpointed deficiencies while achieving high numerical and parallel efficiency at the same time: adaptive Finite Element Method (FEM) approaches and generalised multigrid/domain decomposition solvers of ScaRC type, realised in the FEM package FEAST. The aim of this article is to illustrate how problems from Computational Structural Mechanics (CSM) and Computational Fluid Dynamics (CFD) can be tackled in the FEAST framework. Since this basic library only provides facilities to solve scalar problems, the question is how to treat multi-field simulations. The main focus of the article is concentrated on the design of appropriate preconditioners for the resulting saddle point problems which have a major impact on the numerical efficiency of the underlying iterative algorithms.