Solving Coupled Consolidation Equations

  • Felicja Okulicka-Dłuzewska
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 4310)


The iterative method to solve the equations modelling the coupled consolidation problem is presented. The algorithm is tested in the finite element package Hydro-geo for the geotechnical constructions.


Pore Pressure Iterative Method Conjugate Gradient Method Excess Pore Pressure Virtual Work Principle 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. 1.
    Axelsson, O.: Iterative solution Methods, Cambridge (1994)Google Scholar
  2. 2.
    Axelsson, O., Barker, V.A.: Finite Element Solution of Boundary Value Problems. Academic Press, London (1984)zbMATHGoogle Scholar
  3. 3.
    Barret, R., et al.: Templates for the Solution of Linear Systems: Building Blocks for Iterative Methods. SIAM, Philadelphia (1994)Google Scholar
  4. 4.
    Demmel, J.: Applied numerical linear algebra (1997)Google Scholar
  5. 5.
    Dłuzewski, J.M.: Non-linear consolidation in finite element modelling. In: Proceedings of the Ninth International Conference on Computer Methods and Advances in Geomechanics, Wuhan, China, November (1997)Google Scholar
  6. 6.
    Dłuzewski, J.M.: Nonlinear problems during consolidation process. In: Griffiths, D.V., Gioda, G. (eds.) Advanced Numerical Applications and Plasticity in Geomechanics, Springer, Heidelberg (2001)Google Scholar
  7. 7.
    Dłuzewski, J.M.: HYDRO-GEO - finite element package for geotechnics, hydrotechnics and environmental engineering, Warsaw (in Polish) (1997)Google Scholar
  8. 8.
    Lewis, R.W., Schrefler, B.A.: The Finite Element Method in the Static and Dynamic Deformation and Consolidation of Porous Media. John Wiley and Sons, Chichester (1998)zbMATHGoogle Scholar
  9. 9.
    Okulicka, F.: High-Performance Computing in Geomechanics by a Parallel Finite Element Approach. In: Sørevik, T., et al. (eds.) PARA 2000. LNCS, vol. 1947, pp. 391–398. Springer, Heidelberg (2001)CrossRefGoogle Scholar
  10. 10.
    Okulicka, F.: Parallelization of Finite Element ement Package by MPI library. In: Cotronis, Y., Dongarra, J.J. (eds.) Recent Advances in Parallel Virtual Machine and Message Passing Interface. LNCS, vol. 2131, pp. 425–436. Springer, Heidelberg (2001)Google Scholar
  11. 11.
    Parter, S.: Preconditioning Legrendre spectral collocation methods for elliptic problems I: Finite element operators. SIAM Journal on Numerical Analysis 39(1), 348–362 (2001)zbMATHCrossRefMathSciNetGoogle Scholar
  12. 12.
    Phoon, K.K., Toh, K.C., Chan, S.H., Lee, F.H.: An Efficient Diagonal Preconditioner for Finite Element Solution of Biot’s Consolidation Equations. International Journal of Numerical Methods in EngineeringGoogle Scholar
  13. 13.
    Saad, Y.: Iterative methods for Sparse linear systems. SIAM, Philadelpia (2003)zbMATHGoogle Scholar
  14. 14.
    Wienands, R., et al.: An effcient multigrid solver based on distributive smoothing for poroelasticity equations. Computing 73, 99–119 (2004)zbMATHCrossRefMathSciNetGoogle Scholar

Copyright information

© Springer Berlin Heidelberg 2007

Authors and Affiliations

  • Felicja Okulicka-Dłuzewska
    • 1
  1. 1.Faculty of Mathematics and Information Science, Warsaw University of Technology, Pl. Politechniki 1, 00-661 WarsawPoland

Personalised recommendations