Performance comparisons of geometric multigrid solvers and balancing domain decomposition solvers

Abstract

Multigrid and domain-decomposition methods are now widely used in large-scale simulation studies. Meanwhile, many types of preconditioners are available for speeding the convergence. Users of analysis models are interested in the method or preconditioner that minimizes the computing time. In this paper, we analyze a thermal problem and a solid problem using two free, open-source software programs—the UG4 framework and the ADVENTURE system—based on geometric multigrid (GM) solvers and balancing domain-decomposition (BDD) solvers. We examine and report the computing times and iteration numbers to convergence of the two programs, and generate a common software interface between the UG4 framework and ADVENTURE system. Through this software interface, we can compare the solvers of the two software systems using the same mesh data. The results were presented on the CX400 system at the Information Technology Center of Nagoya University, Japan. The convergence rate of GM solver improved after suitable smoothing and scaling to finer grids. The BDD solver is suitable for large-scale analyses of structures with detailed and complex geometries.