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GEM – A Platform for Advanced Mathematical Geosimulations

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Book cover Parallel Processing and Applied Mathematics (PPAM 2009)

Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 6067))

Abstract

The contribution deals with the development of a 3-D finite-element package called GEM and its aspirations in demanding mathematical modelling and simulations arising in geosciences. On the background of two complex applications from the presently running projects, formulated as linear elasticity and thermo-elasticity problems, the most important characteristics, especially those of the solvers, are presented. Features related to high performance computing, including parallel processing, are focused on.

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References

  1. Nečas, J., Hlaváček, I.: Mathematical Theory of Elastic and Elasto-Plastic Bodies: An Introduction. Elsevier, Amsterdam (1981)

    MATH  Google Scholar 

  2. Blaheta, R.: Displacement decomposition – incomplete factorization preconditioning techniques for linear elasticity problems. Numerical Linear Algebra with Applications 1 (1994)

    Google Scholar 

  3. Quarteroni, A., Valli, A.: Numerical Approximation of Partial Differential Equations. Springer, Berlin (1994)

    MATH  Google Scholar 

  4. Jakl, O.: Database methods in finite element postprocessing. In: Vondrák, I., Štefan, J. (eds.) Proc. Computer Science, VŠB, TU Ostrava (1995)

    Google Scholar 

  5. Blaheta, R.: GPCG – generalized preconditioned CG method and its use with nonlinear and nonsymmeteric displacement decomposition preconditioners. Appl. Math. 9, 527–550 (2002)

    MATH  MathSciNet  Google Scholar 

  6. Blaheta, R.: Space Decomposition Preconditioners and Parallel Solvers. In: Proc. of the 5th European Conference on Numerical Mathematics and Advanced Applications ENUMATH 2003, pp. 20–38. Springer, Berlin (2003)

    Google Scholar 

  7. Blaheta, R., Jakl, O., Starý, J.: Linear system solvers based on space decompositions and parallel computations. Engineering Mechanics 10(6), 439–454 (2003)

    Google Scholar 

  8. Toselli, A., Widlund, O.: Domain Decomposition Methods – Algorithms and Theory. Springer, Heidelberg (2005)

    MATH  Google Scholar 

  9. Blaheta, R., Jakl, O., Starý, J.: Displacement decomposition and parallelization of the PCG method for elasticity problems. Int. J. of Computational Science and Engineering (IJCSE) 1, 183–191 (2005)

    Article  Google Scholar 

  10. Kohut, R., Starý, J., Blaheta, R., Krečmer, K.: Parallel Computing of Thermoelasticity Problems. In: Lirkov, I., Margenov, S., Waśniewski, J. (eds.) LSSC 2005. LNCS, vol. 3743, pp. 671–678. Springer, Heidelberg (2006)

    Chapter  Google Scholar 

  11. Blaheta, R., Byczanski, P., Jakl, O., Kohut, R., Kolcun, A., Krečmer, K., Starý, J.: Large scale parallel FEM computations of far/near stress field changes in rocks. Future Generation Computer Systems 22(4), 449–459 (2006)

    Article  Google Scholar 

  12. Blaheta, R., Kohut, R., Neytcheva, M., Starý, J.: Schwarz Methods for Discrete Elliptic and Parabolic problems with an Application to Nuclear Waste Repository Modelling. Mathematics and Computers in Simulation 76, 18–27 (2007)

    Article  MATH  MathSciNet  Google Scholar 

  13. Andersson, C.: Äspö Hard Rock Laboratory. Äspö Pillar Stability Experiment, final report. SKB TR-07-01, Stockholm (2007)

    Google Scholar 

  14. Jakl, O., Kohut, R., Starý, J.: MPI and OpenMP Computations for Nuclear Waste Deposition Models. In: Wyrzykowski, R., Dongarra, J., Karczewski, K., Wasniewski, J. (eds.) PPAM 2007. LNCS, vol. 4967, pp. 409–418. Springer, Heidelberg (2008)

    Chapter  Google Scholar 

  15. Blaheta, R., Byczanski, P., Kohut, R., Starý, J.: Modelling THM Processes in Rocks with the Aid of Parallel Computing. In: Proc. of the 3rd Int. Conference on Coupled T-H-M-C Processes in Geosystems GeoProc 2008. ISTE and John Wiley, London (2008)

    Google Scholar 

  16. GEM download page, http://www.ugn.cas.cz/link/gem

  17. Singer, S., Nelder, J.: Nelder-Mead algorithm. Scholarpedia 4(7), 2928 (2009), http://www.scholarpedia.org/article/Nelder-Mead_algorithm

    Article  Google Scholar 

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Blaheta, R., Jakl, O., Kohut, R., Starý, J. (2010). GEM – A Platform for Advanced Mathematical Geosimulations. In: Wyrzykowski, R., Dongarra, J., Karczewski, K., Wasniewski, J. (eds) Parallel Processing and Applied Mathematics. PPAM 2009. Lecture Notes in Computer Science, vol 6067. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-14390-8_28

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  • DOI: https://doi.org/10.1007/978-3-642-14390-8_28

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-642-14389-2

  • Online ISBN: 978-3-642-14390-8

  • eBook Packages: Computer ScienceComputer Science (R0)

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