Skip to main content
SpringerLink
Log in

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

  • Published:
Computing and Visualization in Science

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.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Fig. 1
Fig. 2
Fig. 3
Fig. 4
Fig. 5
Fig. 6
Fig. 7
Fig. 8
Fig. 9
Fig. 10

Similar content being viewed by others

References

  1. http://www.lua.org

  2. Bank, R.: Pltmg: a software package for solving elliptic partial differential equations-user’s guide 10.0 (2007)

  3. Bank, R., Rose, D.: Some error estimates for the box method. SIAM J. Numer. Anal. 24(4), 777–787 (1987)

    Article  MATH  MathSciNet  Google Scholar 

  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)

    Book  Google Scholar 

  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)

    Article  MATH  Google Scholar 

  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).

  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)

    Article  MATH  MathSciNet  Google Scholar 

  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)

  9. Birken, K.: Dynamic Distributed Data in a Parallel Programming Environment, DDD, Reference Manual. Rechenzentrum Univ, Stuttgart (1994)

    Google Scholar 

  10. Ciarlet, P., Lions, J.: Finite Element Methods (part 1). North-Holland, Amsterdam (1991)

    MATH  Google Scholar 

  11. Farhat, C., Lesoinne, M., Pierson, K.: A scalable dual-primal domain decomposition method. Numer. Linear Algebra Appl. 7, 687–714 (2000)

    Article  MATH  MathSciNet  Google Scholar 

  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).

  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. Frolkovic, P., Mikula, K.: High-resolution flux-based level set method. SIAM J. Sci. Comput. 29(2), 579–597 (2008)

    Article  MathSciNet  Google Scholar 

  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)

    Article  MATH  Google Scholar 

  16. Gropp, W., Lusk, E., Skjellum, A.: Using MPI: portable parallel programming with the message-passing interface, vol. 1. MIT press (1999).

  17. Hauser, A., Wittum, G.: Parallel large eddy simulation with UG. High Perform. Comput. Sci. Eng. 06, 269–278 (2007)

    Google Scholar 

  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)

  19. Hestenes, M., Stiefel, E.: Methods of conjugate gradients for solving linear systems. J. Res. Natl. Bur. Stand. 49(6), 409–436 (1952)

    Article  MATH  MathSciNet  Google Scholar 

  20. Hoffer: Vrl, in preparation. Computing and visualization in science (2011)

  21. Klawonn, A., Widlund, O.B.: Dual-primal feti methods for linear elasticity. Commun. Pure Appl. Math. 59(11), 1523–1572 (2006)

  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)

    Article  Google Scholar 

  23. Leijnse, A.: Three-dimensional modeling of coupled flow and transport in porous media, PhD thesis. University of Notre Dame, Indiana (1992).

  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)

  25. Naegel, A., Falgout, R.D., Wittum, G.: Filtering algebraic multigrid and adaptive strategies. Comput. Vis. Sci. 11(3), 159–167 (2008)

    Article  MathSciNet  Google Scholar 

  26. Nagele, S., Wittum, G.: Large-eddy simulation and multigrid methods. Electron. Trans. Numer. Anal. 15, 152–164 (2003)

    MathSciNet  Google Scholar 

  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)

    Article  MATH  MathSciNet  Google Scholar 

  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)

  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)

  30. Schmidt, A., Siebert, K.: Design of Adaptive Finite Element Software: The Finite Element Toolbox ALBERTA. Springer, Berlin (2005)

    Google Scholar 

  31. Stüben, K.: A review of algebraic multigrid. Journal of Computational and Applied Mathematics 128(1–2), 281–309 (2001)

  32. Toselli, A., Widlund, O.: Domain Decomposition Methods: Algorithms and Theory. Springer, Berlin (2005)

    Google Scholar 

  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)

    Article  MATH  MathSciNet  Google Scholar 

  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)

    Article  MATH  Google Scholar 

  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)

    Article  Google Scholar 

  36. Wagner, C.: On the algebraic construction of multilevel transfer operators. Computing 65, 73–95 (2000)

    MATH  MathSciNet  Google Scholar 

  37. Wieners, C.: M++. http://www.mathematik.uni-karlsruhe.de/wieners

Download references

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).

Author information

Authors and Affiliations

  1. Goethe Center for Scientific Computing (G-CSC), Goethe University Frankfurt am Main, Kettenhofweg 139, 60325, Frankfurt, Germany

    Andreas Vogel, Sebastian Reiter, Martin Rupp, Arne Nägel & Gabriel Wittum

Authors
  1. Andreas Vogel
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Sebastian Reiter
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Martin Rupp
    View author publications

    You can also search for this author in PubMed Google Scholar

  4. Arne Nägel
    View author publications

    You can also search for this author in PubMed Google Scholar

  5. Gabriel Wittum
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Andreas Vogel.

Additional information

Communicated by: Randolph E. Bank.

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Vogel, A., Reiter, S., Rupp, M. et al. UG 4: A novel flexible software system for simulating PDE based models on high performance computers. Comput. Visual Sci. 16, 165–179 (2013). https://doi.org/10.1007/s00791-014-0232-9

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s00791-014-0232-9

Keywords

Search

Navigation