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Mesh generation for thin layered domains and its application to parallel multigrid simulation of groundwater flow

  • IMG 2016
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Computing and Visualization in Science


The generation of detailed three dimensional meshes for the simulation of groundwater flow in thin layered domains is crucial to capture important properties of the underlying domains and to reach a satisfying accuracy. At the same time, this level of detail poses high demands both on suitable hardware and numerical solver efficiency. Parallel multigrid methods have been shown to exhibit near optimal weak scalability for massively parallel computations of density driven flow. A fully automated parameterized algorithm for prism based meshing of coarse grids from height data of individual layers is presented. Special structures like pinch outs of individual layers are preserved. The resulting grid is used as a starting point for parallel mesh and hierarchy creation through interweaved projected refinement and redistribution. Efficiency and applicability of the proposed approach are demonstrated for a parallel multigrid based simulation of a realistic sample problem.

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  1. Baker, A., Falgout, R., Kolev, T., Yang, U.: Multigrid smoothers for ultra-parallel computing. SIAM J. Sci. Comput. 33, 2864–2887 (2011)

    Article  MathSciNet  Google Scholar 

  2. Bastian, P., Blatt, M., Scheichl, R.: Algebraic multigrid for discontinuous galerkin discretizations of heterogeneous elliptic problems. Numer. Linear Algebra Appl. 19(2), 367–388 (2012)

    Article  MathSciNet  Google Scholar 

  3. Bastian, P., Wittum, G.: Adaptive multigrid methods: the UG concept. In: Notes on Numerical Fluid Mechanics, vol. 46, pp. 17–17 (1994)

  4. Bergen, B., Gradl, T., Rude, U., Hulsemann, F.: A massively parallel multigrid method for finite elements. Comput. Sci. Eng. 8(6), 56–62 (2006)

    Article  Google Scholar 

  5. Chew, L.P.: Constrained delaunay triangulations. Algorithmica 4(1), 97–108 (1989)

    Article  MathSciNet  Google Scholar 

  6. Corbet, T., Knupp, P.: The role of regional groundwater flow in the hydrogeology of the Culebra Member of the Rustler Formation at the Waste Isolation Pilot Plant (Wipp), Southeastern New Mexico. University of North Texas Libraries, Tech. rep. (1996)

  7. de Berg, M., Cheong, O., Van Kreveld, M., Overmars, M.: Computational Geometry: Algorithms and Applications, 3rd edn. Springer, Santa Clara (2008)

    Book  Google Scholar 

  8. Feuchter, D.: Geometrie- und gittererzeugung für anisotrope schichtengebiete. Ph.D. thesis, Universität Heidelberg (2008)

  9. Field, D.A.: Qualitative measures for initial meshes. Int. J. Numer. Methods Eng. 47(4), 887–906 (2000)

    Article  Google Scholar 

  10. Frolkovič, P., De Schepper, H.: Numerical modelling of convection dominated transport coupled with density driven flow in porous media. Adv Water Resour. 24(1), 63–72 (2000)

    Article  Google Scholar 

  11. Gmeiner, B., Köstler, H., Stürmer, M., Rüde, U.: Parallel multigrid on hierarchical hybrid grids: a performance study on current high performance computing clusters. Concurr. Comput. Pract. Exp. 26(1), 217–240 (2014)

    Article  Google Scholar 

  12. Heppner, I., Lampe, M., Nägel, A., Reiter, S., Rupp, M., Vogel, A., Wittum, G.: Software framework ug4: parallel multigrid on the hermit supercomputer. In W. E. Nagel, D. H. Kröner, & M. M. Resch (Eds.), High performance computing in science and engineering ’12: transactions of the High Performance Computing Center, Stuttgart (HLRS), 435–449 (2013)

  13. Johannsen, K.: Numerische aspekte dichtegetriebener strömung in porösen medien. Habilitation (2004)

  14. Hassanizadeh, S.M., Leijnse, T.: On the modeling of brine transport in porous media. Water Resour. Res. 24(3), 321–330 (1988)

    Article  Google Scholar 

  15. Promesh: Accessed June 2017

  16. Reiter, S.: Effiziente algorithmen und datenstrukturen für die realisierung von adaptiven, hierarchischen gittern auf massiv parallelen systemen. Ph.D. thesis, Universität Frankfurt am Main (2014)

  17. Reiter, S., Vogel, A., Heppner, I., Rupp, M., Wittum, G.: A massively parallel geometric multigrid solver on hierarchically distributed grids. Comp. Vis. Sci. 16(4), 151–164 (2013)

    Article  Google Scholar 

  18. Sundar, H., Biros, G., Burstedde, C., Rudi, J., Ghattas, O., Stadler, G.: Parallel geometric–algebraic multigrid on unstructured forests of octrees. In: Proceedings of the International Conference on High Performance Computing, Networking, Storage and Analysis, SC ’12, pp. 43:1–43:11. IEEE Computer Society Press, Los Alamitos, CA (2012)

  19. Vogel, A., Reiter, S., Rupp, M., Nägel, A., Wittum, G.: UG 4: a novel flexible software system for simulating PDE based models on high performance computers. Comp. Vis. Sci. 16(4), 165–179 (2013)

    Article  Google Scholar 

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This work has been supported by the German Ministry of Economics and Technology (BMWi, 02E11476B) and by the DFG Priority Program 1648 Software for Exascale Computing (SPPEXA) in the project Exasolvers (WI 1037/24-2). We thank the HLRS for the opportunity to use Hazel Hen and their kind support. The authors also gratefully acknowledge the Gauss Centre for Supercomputing e.V. ( for funding this project by providing computing time through the John von Neumann Institute for Computing (NIC) on the GCS Supercomputer JUQUEEN at Jülich Supercomputing Centre (JSC).

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Correspondence to Sebastian Reiter.

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Communicated by Babett Lemke.

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Reiter, S., Logashenko, D., Vogel, A. et al. Mesh generation for thin layered domains and its application to parallel multigrid simulation of groundwater flow. Comput. Visual Sci. 23, 2 (2020).

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