Abstract
This contribution deals with numerical upscaling of the elastic material behaviour, namely of geocomposites, from microscale to macroscale through finite element analysis. This computationally demanding task raises many algorithmic and implementation issues related to efficient parallel processing. On the solution of the arising boundary value problem, considered with either Dirichlet or Neumann boundary conditions, we discuss various parallelization strategies, and compare their implementations in the specialized in-house finite element package GEM and through the general numerical solution framework Trilinos.
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References
Arbenz, P., van Lenthe, G.H., Mennel, U., Müller, R., Sala, M.: A scalable multi-level preconditioner for matrix-free μ-finite element analysis of human bone structures. Int. J. Numer. Methods Eng. 73(7), 927–947 (2008)
Blaheta, R.: A multilevel method with overcorrection by aggregation for solving discrete elliptic problems. J. Comput. Appl. Math. 24, 227–239 (1988)
Blaheta, R.: Displacement Decomposition - Incomplete Factorization Preconditioning Techniques for Linear Elasticity Problems. Numerical Linear Algebra with Applications 1, 107–128 (1994)
Blaheta, R.: GPCG - generalized preconditioned CG method and its use with non-linear and non-symmetric displacement decomposition preconditioners. Numerical Linear Algebra with Applications 9, 527–550 (2002)
Blaheta, R.: Space Decomposition Preconditioners and Parallel Solvers. In: Feistauer, M., Dolejíší, V., Knobloch, P., Najzar, K. (eds.) ENUMATH 2003, pp. 20–38. Springer, Berlin (2004)
Blaheta, R., Jakl, O., Kohut, R., Starý, J.: GEM – A Platform for Advanced Mathematical Geosimulations. In: Wyrzykowski, R., Dongarra, J., Karczewski, K., Wasniewski, J. (eds.) PPAM 2009, Part I. LNCS, vol. 6067, pp. 266–275. Springer, Heidelberg (2010)
Blaheta, R., Sokol, V.: Multilevel Solvers with Aggregations for Voxel Based Analysis of Geomaterials. In: Lirkov, I., Margenov, S., Wasniewski, J. (eds.) LSSC 2011. LNCS, vol. 7116, pp. 489–497. Springer, Heidelberg (2012)
Blaheta, R., Hrtus, R., Kohut, R., Axelsson, O., Jakl, O.: Material Parameter Identification with Parallel Processing and Geo-applications. In: Wyrzykowski, R., Dongarra, J., Karczewski, K., Wasniewski, J. (eds.) PPAM 2011, Part I. LNCS, vol. 7203, pp. 366–375. Springer, Heidelberg (2012)
Blaheta, R., Kohut, R., Kolcun, A., Souček, K., Staš, L., Vavro, L.: Digital image based numerical micromechanics of geocomposites with application to chemical grouting (submitted)
Bochev, P., Lehoucq, R.B.: On the Finite Element Solution of the Pure Neumann Problem. SIAM Review 47, 50–66 (2005)
Gee, M.W., Seifert, C.M., Hu, J.J., Tuminaro, R.S., Sala, M.G.: ML 5.0 Smoothed Aggregation User’s Guide. Sandia Report SAND2006-2649 (2006)
Nečas, J., Hlaváček, I.: Mathematical theory of elastic and elasto-plastic bodies: an introduction. Elsevier, Amsterdam (1981)
Saad, Y.: Iterative Methods for Sparse Linear Systems. SIAM, Philadelphia (2003)
Vaněk, P., Mandel, J., Brezina, M.: Algebraic Multigrid by Smoothed Aggregation for Second and Fourth Order Elliptic Problems. Computing 56, 179–196 (1996)
Zohdi, T.J., Wriggers, P.: An Introduction to Computational Micromechanics. Springer, Berlin (2005, 2008)
The Trilinos Project Home Page. Sandia National Laboratories (2012), http://trilinos.sandia.gov/
IFPACK Home. IFPACK Object-Oriented Algebraic Preconditioner Package, Sandia National Laboratories (2012), http://trilinos.sandia.gov/packages/ifpack/
ML Home. ML: Multi Level Preconditioning Package, Sandia National Laboratories (2012), http://trilinos.sandia.gov/packages/ml/
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Blaheta, R., Jakl, O., Starý, J., Turan, E. (2013). Parallel Solvers for Numerical Upscaling. In: Manninen, P., Öster, P. (eds) Applied Parallel and Scientific Computing. PARA 2012. Lecture Notes in Computer Science, vol 7782. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-36803-5_27
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DOI: https://doi.org/10.1007/978-3-642-36803-5_27
Publisher Name: Springer, Berlin, Heidelberg
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