Abstract
The modeling of physical phenomena in a variety of fields of scientific interest lead to a formulation in terms of partial differential equations. Especially when complex geometries as the domain of definition are involved, a direct and exact solution is not accessible, but numerical schemes are used to compute an approximate discrete solution. In this report, we focus on elliptic and parabolic types of equations that include spatial operators of second order. When discretizing such problems using commonly known discretization schemes such as finite element methods or finite volume methods, large systems of linear equations arise naturally. Their solution takes the largest amount of the overall computing time.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
References
C. Farhat, M. Lesoinne, P. LeTallec, K. Pierson, and D. Rixen. Feti-dp: a dual-primal unified feti method - part i: A faster alternative to the two-level feti method. International Journal for Numerical Methods in Engineering, 50(7):1523–1544, 2001.
P. Frolkovic. Finite volume discretizations of density driven flows in porous media. Vilsmeier R. Benkhaldoun F., editor, Finite Volumes for Complex Applications, pages 433–440, 1996.
W. Hackbusch. Multi-grid methods and applications, vol. 4 of springer series in computational mathematics, 1985.
A. Klawonn and O. Rheinbach. Highly scalable parallel domain decomposition methods with an application to biomechanics. ZAMM - Journal of Applied Mathematics and Mechanics / Zeitschrift für Angewandte Mathematik und Mechanik, 90(1):5–32, 2010.
A. Leijnse. Three-dimensional modeling of coupled flow and transport in porous media. 1992.
A. Naegel, R. D. Falgout, and G. Wittum. Filtering algebraic multigrid and adaptive strategies. Computing and Visualization in Science, 11(3):159–167, 2008.
S. Reiter, A. Vogel, I. Heppner, M. Rupp, and G. Wittum. A massively parallel geometric multigrid solver on hierarchically distributed grids. Computing and Visualization in Science, 2012, in press.
J. W. Ruge and K. Stüben. Multgrid Methods, volume 3 of Frontiers in Applied Mathematics, chapter Algebraic multigrid (AMG), pages 73–130. SIAM, Philadelphia, PA, 1987.
A. Vogel, S. Reiter, M. Rupp, A. Nägel, and G. Wittum. Ug 4 - a novel flexible software system for simulating pde based models on high performance computers. Computing and Visualization in Science, 2012, in press.
C.I. Voss and W.R. Souza. Variable density flow and solute transport simulation of regional aquifers containing a narrow freshwater-saltwater transition zone. Water Resources Research, 23(10):1851–1866, 1987.
C. Wagner. On the algebraic construction of multilevel transfer operators. Computing, 65:73–95, 2000.
Acknowledgements
This work has been supported by the Goethe-Universität Frankfurt and by the German Ministry of Economy and Technology (BMWi) via grant 02E10326 and grant 02E10568. We thank the HLRS for the opportunity to use Hermit and their kind support.
Author information
Authors and Affiliations
Corresponding author
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2013 Springer-Verlag Berlin Heidelberg
About this paper
Cite this paper
Heppner, I. et al. (2013). Software Framework ug4: Parallel Multigrid on the Hermit Supercomputer. In: Nagel, W., Kröner, D., Resch, M. (eds) High Performance Computing in Science and Engineering ‘12. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-33374-3_32
Download citation
DOI: https://doi.org/10.1007/978-3-642-33374-3_32
Published:
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-642-33373-6
Online ISBN: 978-3-642-33374-3
eBook Packages: Mathematics and StatisticsMathematics and Statistics (R0)