Abstract
We introduce a general parallel model for solving coupled nonlinear and time-dependent problems in soil mechanics, where we employ general purpose linear solvers with specially adjusted preconditioners. In particular, we present a parallel realization of the GMRES method applied to a triphasic porous media model in soil mechanics, where we compute the deformation of unsaturated soil together with the pore-fluid flow of water and air in the soil. Therefore, we propose a pointwise preconditioner coupling all unknowns at the nodal points. In two large-scale numerical experiments we finally present an extended evaluation of our parallel model for demanding configurations of the triphasic model.
Article PDF
Similar content being viewed by others
Avoid common mistakes on your manuscript.
References
Barrett R, Berry M, Chan T, Demmel J, Donato J, Dongarra J, Eijkhout V, Pozo R, Romine C, van der Vorst H (1994) Templates for the solution of linear systems. SIAM, Philadelphia, ftp://ftp.netlib.org/templates/templates.ps
Bastian P (1996) Parallele adaptive Mehrgitterverfahren. Teubner Skripten zur Numerik. Teubner, Stuttgart
de Boer R (2000) Theory of Porous Media. Springer-Verlag, Berlin
Ehlers W (1995) A single-surface yield function for geomaterials. Archive of Applied Mech 65:246–259
Ehlers W (2002) Foundations of multiphasic and porous materials. In Ehlers W, Bluhm J (eds) Porous Media: Theory, Experiments and Numerical Applications. Springer-Verlag, Berlin pp. 3–86
Ehlers W, Graf T, Ammann M (2004) Deformation and localization analysis in partially saturated soil. Computer Methods in Applied Mech Eng 193:2885–2910
Helmig R (1997) Multiphase Flow and Transport Processes in the Subsurface. Springer-Verlag, Berlin
Helmig R, Huber R (1998) Comparison of Galerkin-type discretization techniques for two-phase flow in heterogeneous porous media. Advances in Water Resources, 21:697–711
Lewis RW, Schrefler BA (1998) The Finite Element Method in the Static and Dynamic Deformation and Consolidation of Porous Media, 2 nd Edition. Wiley, Chichester
Mahnkopf D (2000) Lokalisierung fluidgesättigter poröser Festkörper bei finiten elastoplastischen Deformationen. Dissertation, Bericht Nr. II-5 aus dem Institut für Mechanik (Bauwesen), Universität Stuttgart
Müllerschön H (2000) Spannungs-Verzerrungsverhalten granularer Materialien am Beispiel von Berliner Sand. Dissertation, Bericht Nr. II-6 aus dem Institut für Mechanik (Bauwesen), Universität Stuttgart
Perzyna P (1966) Fundamental problems in viscoplasticity. Advances in Applied Mech 9:243–377
Schöberl J (1997) NETGEN – an advancing front 2d/3d-mesh generator based on abstract rules. Computing and Visualization in Science 1:40–52
Stroud AH (1971) Approximate Calculation of Multiple Integrals. Prentice-Hall, New Jersey
van Genuchten MT (1980) A closed-form equation for predicting the hydraulic conductivity of unsaturated soils. Soil Science Society of America J. 44:892–898
Wieners C, Ammann M, Diebels S, Ehlers W (2002) Parallel 3-d simulations for porous media models in soil mechanics. Comput Mech 29:73–87
Wieners C, Ammann M, Ehlers W (2004) Distributed Point Objects: A new concept for parallel finite elements applied to a geomechanical problem. Future Generation Computer Systems, in press
Author information
Authors and Affiliations
Corresponding author
Rights and permissions
About this article
Cite this article
Wieners, C., Graf, T., Ammann, M. et al. Parallel Krylov methods and the application to 3-d simulations of a triphasic porous media model in soil mechanics. Comput Mech 36, 409–420 (2005). https://doi.org/10.1007/s00466-004-0654-1
Received:
Accepted:
Published:
Issue Date:
DOI: https://doi.org/10.1007/s00466-004-0654-1