On consistency, stability and convergence of staggered solution procedures

Ewa Turska; Bernardo A. Schrefler

Atti della Accademia Nazionale dei Lincei. Classe di Scienze Fisiche, Matematiche e Naturali. Rendiconti Lincei. Matematica e Applicazioni (1994)

  • Volume: 5, Issue: 3, page 265-271
  • ISSN: 1120-6330

Abstract

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The simultaneous and staggered procedures of solving a partitioned form of a coupled system of ordinary differential equations are presented. Formulas for errors are compared. Counter-examples for convergence with a constant number of iterations at each time step are given.

How to cite

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Turska, Ewa, and Schrefler, Bernardo A.. "On consistency, stability and convergence of staggered solution procedures." Atti della Accademia Nazionale dei Lincei. Classe di Scienze Fisiche, Matematiche e Naturali. Rendiconti Lincei. Matematica e Applicazioni 5.3 (1994): 265-271. <http://eudml.org/doc/244163>.

@article{Turska1994,
abstract = {The simultaneous and staggered procedures of solving a partitioned form of a coupled system of ordinary differential equations are presented. Formulas for errors are compared. Counter-examples for convergence with a constant number of iterations at each time step are given.},
author = {Turska, Ewa, Schrefler, Bernardo A.},
journal = {Atti della Accademia Nazionale dei Lincei. Classe di Scienze Fisiche, Matematiche e Naturali. Rendiconti Lincei. Matematica e Applicazioni},
keywords = {Coupled problems; Systems of linear simultaneous equations; Numerical solution procedures; consistency; stability; staggered solution procedures; counterexamples; system of ordinary differential equations; convergence},
language = {eng},
month = {9},
number = {3},
pages = {265-271},
publisher = {Accademia Nazionale dei Lincei},
title = {On consistency, stability and convergence of staggered solution procedures},
url = {http://eudml.org/doc/244163},
volume = {5},
year = {1994},
}

TY - JOUR
AU - Turska, Ewa
AU - Schrefler, Bernardo A.
TI - On consistency, stability and convergence of staggered solution procedures
JO - Atti della Accademia Nazionale dei Lincei. Classe di Scienze Fisiche, Matematiche e Naturali. Rendiconti Lincei. Matematica e Applicazioni
DA - 1994/9//
PB - Accademia Nazionale dei Lincei
VL - 5
IS - 3
SP - 265
EP - 271
AB - The simultaneous and staggered procedures of solving a partitioned form of a coupled system of ordinary differential equations are presented. Formulas for errors are compared. Counter-examples for convergence with a constant number of iterations at each time step are given.
LA - eng
KW - Coupled problems; Systems of linear simultaneous equations; Numerical solution procedures; consistency; stability; staggered solution procedures; counterexamples; system of ordinary differential equations; convergence
UR - http://eudml.org/doc/244163
ER -

References

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  1. SIMONI, L. - SCHREFLER, B. A., A staggered F. E. solution for water and gas flow in deforming porous media. Commun. Appl. Num. Methods, 7, 1991, 213-223. Zbl0724.76052
  2. LAMBERT, J. D., Computational Methods in Ordinary Differential Equations. J. Wiley & Sons, London1973. Zbl0258.65069MR423815
  3. TURSKA, E. - WISNIEWSKI, K. - SCHREFLER, B. A., Error propagation of staggered solution procedures for transient problems. Accepted for publication in Comp. Meth. in Appl. Mech. and Engng. 
  4. PARK, K. C., Stabilisation of partitioned solution procedure for pore fluid-soil interaction analysis. Int. J. Num. Meth. in Engng., 19, 1983, 1669-1673. Zbl0519.76095
  5. PARK, K. C., Partitioned transient analysis procedures for coupled-field problems: stability analysis. ASME J. Appl. Mech., 47, 1980, 370-376. Zbl0437.73072MR574231
  6. ZIENKIEWICZ, O. C. - PAUL, D. K. - CHAN, A. H. C., Unconditionally stable staggered solution procedure for soil-pore fluid interaction problems. Int. J. Num. Meth. in Engng., 26, 1988, 1039-1055. Zbl0634.73110
  7. PARK, K. C. - FELIPPA, C. A., Partitioned analysis of coupled systems. In: T. BELYTSCHKO - T. J. R. HUGHES (eds.), Computational Methods for Transient Analysis. Elsevier Science Publishers B. V., 1983. Zbl0546.73063
  8. ZIENKIEWICZ, O. C. - TAYLOR, R. L., The Finite Element Method. Vol. 2, McGraw-Hill, London1991. Zbl0974.76003
  9. GEAR, C. W., Numerical Initial Value Problems in Ordinary Differential Equations. Prentice-Hall Inc., Engelwood Cliffs, N.J.1971. Zbl1145.65316MR315898
  10. HUGHES, T. J. R., The Finite Element Method. Prentice-Hall Inc., Engelwood Cliffs, N.J.1987. Zbl0634.73056MR1008473
  11. WANNER, G., A short proof on non-linear A-stability. BIT, 16, 1976, 226-227. Zbl0329.65048MR416037

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