On convergence conditions of partitioned solution procedures for consolidation problems

Abstract A systematic approach to determine conditions for convergence of partitioned staggered procedures for consolidation problems is presented. Consistency, convergence and stability is investigated for linear and nonlinear problems and a comparison of the partitioned and direct method is made. Conclusions, based also on numerical evidence, are drawn. The significance of the ratio of the time step length to the square of the finite element mesh length is shown.

[1]  R. D. Richtmyer,et al.  Difference methods for initial-value problems , 1959 .

[2]  John Ll. Morris Computational Methods in Elementary Numerical Analysis , 1983 .

[3]  Li Xikui Finite‐element analysis for immiscible two‐phase fluid flow in deforming porous media and an unconditionally stable staggered solution , 1990 .

[4]  O. C. Zienkiewicz,et al.  Unconditionally stable staggered solution procedure for soil-pore fluid interaction problems , 1988 .

[5]  Charbel Farhat,et al.  A consistency analysis of a class of concurrent transient implicit/explicit algorithms , 1990 .

[6]  O. C. Zienkiewicz,et al.  Coupled Problems and Their Numerical Solution , 1989 .

[7]  Carlos A. Felippa,et al.  Staggered transient analysis procedures for coupled mechanical systems: Formulation , 1980 .

[8]  Bernhard A. Schrefler,et al.  The Finite Element Method in the Deformation and Consolidation of Porous Media , 1987 .

[9]  L. B. Rall,et al.  Computational Solution of Nonlinear Operator Equations , 1969 .

[10]  Nikolaĭ Stepanovich Kurpelʹ Projection-Iterative Methods for Solution of Operator Equations , 1976 .

[11]  Ismael Herrera,et al.  Numerical Modeling in Science and Engineering , 1988 .

[12]  Bernhard A. Schrefler,et al.  A staggered finite-element solution for water and gas flow in deforming porous media , 1991 .

[13]  James M. Ortega,et al.  Iterative solution of nonlinear equations in several variables , 2014, Computer science and applied mathematics.