Advertisement

Computing and Visualization in Science

, Volume 16, Issue 4, pp 165–179 | Cite as

UG 4: A novel flexible software system for simulating PDE based models on high performance computers

  • Andreas Vogel
  • Sebastian Reiter
  • Martin Rupp
  • Arne Nägel
  • Gabriel Wittum
Article

Abstract

In this paper we describe the concept of the renewed software package UG, that is used as a flexible simulation framework for the solution of partial differential equations. A general overview of the concepts of the new implementation is given: The modularization of the software package into several libraries libGrid, libAlgebra, libDiscretization and pcl is described and all major modules are discussed in detail. User backends through scripting and visual editing are briefly considered and examples show the new features of the current implementation.

Keywords

Simulation framework Unstructured grids Multigrid Parallelization 

Notes

Acknowledgments

This work has been supported by the Goethe Universität Frankfurt, the German Ministry of Economy and Technology (BMWi) via grant 02E10568, the German Ministry of Education and Research (BMBF) via grant 02E10326 and 01IH08014A, and the DFG by grants No. WI 1037/24-1 and WI 1037/25-1. The authors gratefully acknowledge the Gauss Centre for Supercomputing (GCS) for providing computing time through the John von Neumann Institute for Computing (NIC) on the GCS share of the supercomputer JUGENE at Jülich Supercomputing Centre (JSC). GCS is the alliance of the three national supercomputing centres HLRS (Universität Stuttgart), JSC (Forschungszentrum Jülich), and LRZ (Bayerische Akademie der Wissenschaften), funded by the German Federal Ministry of Education and Research (BMBF) and the German State Ministries for Research of Baden-Württemberg (MWK), Bayern (StMWFK) and Nordrhein-Westfalen (MIWF).

References

  1. 1.
  2. 2.
    Bank, R.: Pltmg: a software package for solving elliptic partial differential equations-user’s guide 10.0 (2007)Google Scholar
  3. 3.
    Bank, R., Rose, D.: Some error estimates for the box method. SIAM J. Numer. Anal. 24(4), 777–787 (1987)CrossRefzbMATHMathSciNetGoogle Scholar
  4. 4.
    Barrett, R., Berry, M., Chan, T.F., Demmel, J., Donato, J., Dongarra, J., Eijkhout, V., Pozo, R., Romine, C., der Vorst, H.V.: Templates for the Solution of Linear Systems: Building Blocks for Iterative Methods, 2nd edn. SIAM, Philadelphia (1994)CrossRefGoogle Scholar
  5. 5.
    Bastian, P., Birken, K., Johannsen, K., Lang, S., Neuss, N., Rentz-Reichert, H., Wieners, C.: UG-A flexible software toolbox for solving partial differential equations. Comput. Vis. Sci. 1(1), 27–40 (1997)CrossRefzbMATHGoogle Scholar
  6. 6.
    Bastian, P., Birken, K., Johannsen, K., Lang, S., Reichenberger, V., Wieners, C., Wittum, G., Wrobel, C.: Parallel solution of partial differential equations with adaptive multigrid methods on unstructured grids. In: High performance computing in science and engineering, pp. 506–519. Jäger, W. and Krause, E. (2000).Google Scholar
  7. 7.
    Bastian, P., Blatt, M., Dedner, A., Engwer, C., Klöfkorn, R., Ohlberger, M., Sander, O.: A generic grid interface for parallel and adaptive scientific computing. Part I: abstract framework. Computing 82(2), 103–119 (2008)CrossRefzbMATHMathSciNetGoogle Scholar
  8. 8.
    Bastian, P., Wittum, G.: Robustness and adaptivity: The ug concept. In: Hemker, P., Wesseling, P. (eds.) Multigrid Methods IV, Proceedings of the fourth European multigrid conference, Amsterdam, 1993, pp. 1–17. Birkhäuser, Basel (1994)Google Scholar
  9. 9.
    Birken, K.: Dynamic Distributed Data in a Parallel Programming Environment, DDD, Reference Manual. Rechenzentrum Univ, Stuttgart (1994)Google Scholar
  10. 10.
    Ciarlet, P., Lions, J.: Finite Element Methods (part 1). North-Holland, Amsterdam (1991)zbMATHGoogle Scholar
  11. 11.
    Farhat, C., Lesoinne, M., Pierson, K.: A scalable dual-primal domain decomposition method. Numer. Linear Algebra Appl. 7, 687–714 (2000)CrossRefzbMATHMathSciNetGoogle Scholar
  12. 12.
    Frolkovic, P.: Finite volume discretizations of density driven flows in porous media. Vilsmeier R. Benkhaldoun F., editor, Finite volumes for complex applications pp. 433–440 (1996).Google Scholar
  13. 13.
    Frolkovic, P., Logashenko, D., Wittum, G.: Flux-based Level Set Method for Two-phase Flow. Finite Volumes for Complex Applications. ISTE and Wiley, London (2008)Google Scholar
  14. 14.
    Frolkovic, P., Mikula, K.: High-resolution flux-based level set method. SIAM J. Sci. Comput. 29(2), 579–597 (2008)CrossRefMathSciNetGoogle Scholar
  15. 15.
    Grillo, A., Lampe, M., Wittum, G.: Three-dimensional simulation of the thermohaline-driven buoyancy of a brine parcel. Comput. Vis. Sci. 13, 287–297 (2010)CrossRefzbMATHGoogle Scholar
  16. 16.
    Gropp, W., Lusk, E., Skjellum, A.: Using MPI: portable parallel programming with the message-passing interface, vol. 1. MIT press (1999).Google Scholar
  17. 17.
    Hauser, A., Wittum, G.: Parallel large eddy simulation with UG. High Perform. Comput. Sci. Eng. 06, 269–278 (2007)Google Scholar
  18. 18.
    Heroux, M., Bartlett, R., Howle, V., Hoekstra, R., Hu, J., Kolda, T., Lehoucq, R., Long, K., Pawlowski, R., Phipps, E., et al.: An overview of the trilinos project. ACM Trans. Math. Softw. (TOMS) 31(3), 397–423 (2005)Google Scholar
  19. 19.
    Hestenes, M., Stiefel, E.: Methods of conjugate gradients for solving linear systems. J. Res. Natl. Bur. Stand. 49(6), 409–436 (1952)CrossRefzbMATHMathSciNetGoogle Scholar
  20. 20.
    Hoffer: Vrl, in preparation. Computing and visualization in science (2011)Google Scholar
  21. 21.
    Klawonn, A., Widlund, O.B.: Dual-primal feti methods for linear elasticity. Commun. Pure Appl. Math. 59(11), 1523–1572 (2006)Google Scholar
  22. 22.
    Lang, S., Wittum, G.: Large-scale density-driven flow simulations using parallel unstructured grid adaptation and local multigrid methods. Concurr. Comput. Pract. Exper. 17(11), 1415–1440 (2005)CrossRefGoogle Scholar
  23. 23.
    Leijnse, A.: Three-dimensional modeling of coupled flow and transport in porous media, PhD thesis. University of Notre Dame, Indiana (1992).Google Scholar
  24. 24.
    Muha, I., Naegel, A., Stichel, S., Grillo, A., Heisig, M., Wittum, G.: Effective diffusivity in membranes with tetrakaidekahedral cells and implications for the permeability of human stratum corneum. J. Membr. Sci. (2010)Google Scholar
  25. 25.
    Naegel, A., Falgout, R.D., Wittum, G.: Filtering algebraic multigrid and adaptive strategies. Comput. Vis. Sci. 11(3), 159–167 (2008)CrossRefMathSciNetGoogle Scholar
  26. 26.
    Nagele, S., Wittum, G.: Large-eddy simulation and multigrid methods. Electron. Trans. Numer. Anal. 15, 152–164 (2003)MathSciNetGoogle Scholar
  27. 27.
    Nägele, S., Wittum, G.: On the influence of different stabilisation methods for the incompressible navier-stokes equations. J. Comput. Phys. 224(1), 100–116 (2007)CrossRefzbMATHMathSciNetGoogle Scholar
  28. 28.
    Reiter, S., Vogel, A., Heppner, I., Rupp, M., Wittum, G.: A massively parallel geometric multigrid solver on hierarchically distributed grids. Comput. Vis. Sci. (2012, submitted)Google Scholar
  29. 29.
    Ruge, J.W., Stüben, K.: Multgrid Methods, Frontiers in Applied Mathematics, vol. 3, chap. Algebraic multigrid (AMG), pp. 73–130. SIAM, Philadelphia, PA (1987)Google Scholar
  30. 30.
    Schmidt, A., Siebert, K.: Design of Adaptive Finite Element Software: The Finite Element Toolbox ALBERTA. Springer, Berlin (2005)Google Scholar
  31. 31.
    Stüben, K.: A review of algebraic multigrid. Journal of Computational and Applied Mathematics 128(1–2), 281–309 (2001)Google Scholar
  32. 32.
    Toselli, A., Widlund, O.: Domain Decomposition Methods: Algorithms and Theory. Springer, Berlin (2005)Google Scholar
  33. 33.
    Vogel, A., Xu, J., Wittum, G.: A generalization of the vertex-centered finite volume scheme to arbitrary high order. Comput. Vis. Sci. 13(5), 221–228 (2010)CrossRefzbMATHMathSciNetGoogle Scholar
  34. 34.
    Van der Vorst, H.: Bi-cgstab: a fast and smoothly converging variant of bi-cg for the solution of nonsymmetric linear systems. SIAM J. Sci. Stat. Comput. 13, 631 (1992)CrossRefzbMATHGoogle Scholar
  35. 35.
    Voss, C., Souza, W.: Variable density flow and solute transport simulation of regional aquifers containing a narrow freshwater-saltwater transition zone. Water Resour. Res. 23(10), 1851–1866 (1987)CrossRefGoogle Scholar
  36. 36.
    Wagner, C.: On the algebraic construction of multilevel transfer operators. Computing 65, 73–95 (2000)zbMATHMathSciNetGoogle Scholar
  37. 37.

Copyright information

© Springer-Verlag Berlin Heidelberg 2014

Authors and Affiliations

  • Andreas Vogel
    • 1
  • Sebastian Reiter
    • 1
  • Martin Rupp
    • 1
  • Arne Nägel
    • 1
  • Gabriel Wittum
    • 1
  1. 1.Goethe Center for Scientific Computing (G-CSC)Goethe University Frankfurt am MainFrankfurtGermany

Personalised recommendations