Performance comparisons of geometric multigrid solvers and balancing domain decomposition solvers

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.

[1]  George Biros,et al.  A Parallel Geometric Multigrid Method for Finite Elements on Octree Meshes , 2010, SIAM J. Sci. Comput..

[2]  Alfio Quarteroni,et al.  Domain Decomposition Methods for Partial Differential Equations , 1999 .

[3]  Gabriel Wittum,et al.  UG 4: A novel flexible software system for simulating PDE based models on high performance computers , 2013, Comput. Vis. Sci..

[4]  Shinobu Yoshimura,et al.  Advanced general-purpose computational mechanics system for large-scale analysis and design , 2002 .

[5]  Jacques Periaux,et al.  Domain decomposition methods for nonlinear problems in fluid dynamics , 1983 .

[6]  Muneo Hori,et al.  Large-Scale Seismic Response Analysis of a Super-High-Rise-Building Fully Considering the Soil–Structure Interaction Using a High-Fidelity 3D Solid Element Model , 2016 .

[7]  Hari Sundar,et al.  Parallel geometric-algebraic multigrid on unstructured forests of octrees , 2012, 2012 International Conference for High Performance Computing, Networking, Storage and Analysis.

[8]  Ulrich Rüde,et al.  A Massively Parallel Multigrid Method for Finite Elements , 2006, Computing in Science & Engineering.

[9]  Wolfgang Hackbusch,et al.  Multi-grid methods and applications , 1985, Springer series in computational mathematics.

[10]  Hiroshi Kanayama,et al.  Heat Conductive Analysis with Balancing Domain Decomposition Method , 2003 .

[11]  Hiroshi Kawai,et al.  Performance Evaluation of ADVENTURE on K Computer , 2013 .

[12]  Hiroshi Kanayama,et al.  Large Scale Finite Element Analysis with a Balancing Domain Decomposition Method , 2003 .

[13]  Genki Yagawa,et al.  Parallel finite elements on a massively parallel computer with domain decomposition , 1993 .

[14]  Marian Brezina,et al.  Balancing domain decomposition for problems with large jumps in coefficients , 1996, Math. Comput..

[15]  Gabriel Wittum,et al.  A massively parallel geometric multigrid solver on hierarchically distributed grids , 2013, Comput. Vis. Sci..