Standard staggered and staggered Newton schemes in thermo-hydro-mechanical problems

Computer Methods in Applied Mechanics and Engineering

Volumn 144, Issue 1-2, 1997, Pages 93-109

  Schrefler, B A ^a   Simoni, L ^a   Turska, E ^b  

^a UNIVERSITY OF PADOVA   (Italy)

^b POLISH ACADEMY OF SCIENCES   (Poland)

Author keywords

[No Author keywords available]

Indexed keywords

ALGORITHMS; INTEGRATION; ITERATIVE METHODS;

STAGGERED ALGORITHMS; STAGGERED NEWTON METHOD; THERMOHYDROMECHANICAL PROBLEMS;

CONVERGENCE OF NUMERICAL METHODS;

EID: 0031141175     PISSN: 00457825     EISSN: None     Source Type: Journal    
DOI: 10.1016/S0045-7825(96)01170-X     Document Type: Article

References (25)

1. L. Simoni and B.A. Schrefler, A staggered F.E. solution for water and gas flow in deforming porous media, Comm. Appl. Numer. Methods 7 (1991) 213-223.
2. E. Turska and B.A. Schrefler, On convergence conditions of partitioned solution procedures for consolidation problems, Comput. Methods Appl. Mech. Engrg. 106(1-2) (1993) 51-64.
3. R.W. Lewis and B.A. Schrefler, The Finite Element Method in the Deformation and Consolidation of Porous Media (J. Wiley & Sons, Chichester, 1987).
4. O.C. Zienkiewics and A.H.C. Chan, Coupled problems and their numerical solution, in: J.St. Doltisnis, ed., Advances in Computational Nonlinear Mechanics (CISM Lecture Notes, Springer Verlag-Wien, 1989).
5. K.C. Park, Stabilization of partitioned solution procedure for pore fluid-soil interaction analysis, Int. J. Numer. Methods Engrg. 19 (1983) 1669-1673.
6. O.C. Zienkiewicz, D.K. Paul and A.H.C. Chan, Unconditionally stable staggered solution procedure for soil-pore fluid interaction problems, Int. J. Numer. Methods Engrg. 26 (1988) 1039-1055.
7. K.C. Park, Partitioned transient analysis procedures for coupled-field problems: stability analysis, ASME J. Appl. Mech. 47 (1980) 370-376.
8. K.C. Park and C.A. Felippa, Partitioned analysis of coupled systems, in: T. Belytschko and T.J.R. Hughes, eds., Computational Methods for Transient Analysis (Elsevier Science Publishers B.V., 1983).
9. E. Turska, K. Wisniewski and B.A. Schrefler, Error propagation of staggered solution procedures for transient problems, Comput. Methods Appl. Mech. Engrg. 114 (1993) 51-63.
10. G.F. Carey, Parallelism in finite element modelling, Comm. Appl. Numer. Methods 2(3) (1986) 281-288.
11. F. Armero and J.C. Simo, A new unconditionally stable fractional step method for non-linear coupled thermo-mechanical problems, Int. J. Numer. Methods Engrg. 35 (1992) 737-766.
12. N.N. Yanenko, Method of Fractional Steps for Solving Multi-Dimensional Problems of Mathematical Physics, Novosibirsk: Nauka (1967) [in Russian].
13. G.I. Marchuk, Methods of Numerical Analysis (Springer-Verlag, New York, 1975.
14. A.J. Chorin et al., Product formulas and numerical algorithms, Comm. Pure Appl. Math. XXXI (1978) 205-256.
15. C. Miehe, Zur numerischen Behandlung thermomechanischer Prozesse, Forschungs- und Seminarberichte aus dem Bereich der Mechanik der Universtat Hannover, Bericht-Nr. F 88/6 (1988).
16. G. Strang, Approximating semigroups and the consistency of difference methods, Proc. Am. Math. Soc. 20 (1969) 1-7.
17. C. Miehe, E. Stein and P. Wriggers, A general concept for thermomechanical coupling, in: S.N. Atluri and G. Yagawa, eds., Computational Mechanics 88, Proceedings of ICES Conference, Atlanta (Springer-Verlag, Berlin, 1988).
18. J.C. Simo and C. Miehe, Associative coupled thermoplasticity at finite strains: formulation, numerical analysis and implementation, Comput. Methods Appl. Mech. Engrg. 98 (1992) 41-104.
19. P. Wriggers, C. Miehe, M. Kleiber and J.C. Simo, On the coupled thermomechanical treatment of necking problems via finite element methods, Int. J. Numer. Methods Engrg. 33 (1993) 869-883.
20. D. Gawin, P. Baggio and B.A. Schrefler, Coupled heat, water and gas flow in deformable porous media, Int. J. Numer. Methods Fluids 20 (1995) 969-987.
21. B.A. Schrefler and L. Simoni, A unified approach to the analysis of saturated-unsaturated elastoplastic porous media, in: G. Swoboda, ed., Numerical Methods in Geomechanics, Innsbruck 1988 (Balkema, Rotterdam, 1988) 205-212.
22. T.N. Narashimhan and P.A. Witherspoon, Numerical model for saturated-unsaturated flow in deformable porous media. 3 Applications. Water Resour. Res. 14 (1978) 1017-1034.
23. R.W. Lewis, B.A. Schrefler and L. Simoni, Coupling versus uncoupling in soil consolidation, Int. J. Numer. Methods Geomech. 15 (1991) 533-548.
24. N.M. Safai and G.F. Pinder, Vertical and horizontal land deformation in a desaturating porous medium, Adv. Water Res. 2 (1979) 19-25.
25. E. Turska and B.A. Schrefler, On consistency, stability and convergence of staggered solution procedures, Atti Acc. Naz. Lincei, IX, V (1994) 265-271.