Multigrid Methods for Unilateral Contact Problems with Friction

In this paper, multigrid methods are tested on unilateral problems with friction. An optimal strategy is presented and efficiency of the solver is discussed on several examples.

[1]  P. Alart,et al.  A mixed formulation for frictional contact problems prone to Newton like solution methods , 1991 .

[2]  M. Cocu,et al.  Formulation and approximation of quasistatic frictional contact , 1996 .

[3]  P. Panagiotopoulos Inequality problems in mechanics and applications , 1985 .

[4]  R. Hoppe Multigrid Algorithms for Variational Inequalities , 1987 .

[5]  J. Mandel,et al.  Etude algébrique d'une méthode multigrille pour quelques problèmes de frontière libre , 1984 .

[6]  K. Stüben,et al.  Multigrid methods: Fundamental algorithms, model problem analysis and applications , 1982 .

[7]  Wolfgang Hackbusch,et al.  Multi-grid methods and applications , 1985, Springer series in computational mathematics.

[8]  P. M. deZeeuw,et al.  Some implementations of multigrid linear system solvers , 1984 .

[9]  W. Hackbusch,et al.  On multi-grid methods for variational inequalities , 1983 .

[10]  J. Lions,et al.  Inequalities in mechanics and physics , 1976 .

[11]  D. J. Paddon,et al.  Multigrid Methods for Integral and Differential Equations. , 1987 .

[12]  Peter Wriggers,et al.  An algebraic multigrid solver for finite element computations in solid mechanics , 1997 .

[13]  M. Raous,et al.  Quasistatic Signorini Problem with Coulomb Friction and Coupling to Adhesion , 1999 .

[14]  Patrick Chabrand,et al.  Various numerical methods for solving unilateral contact problems with friction , 1998 .

[15]  D. Bai Multigrid Methods for Integral and Differential Equations (D. J. Paddon and H. Holstein, eds.) , 1987 .

[16]  P. Alart,et al.  Solution of frictional contact problems using ILU and coarse/fine preconditioners , 1995 .

[17]  A. Brandt,et al.  Multigrid Algorithms for the Solution of Linear Complementarity Problems Arising from Free Boundary Problems , 1983 .

[18]  Michel Raous,et al.  Remarks on a Numerical Method for Unilateral Contact Including Friction , 1991 .

[19]  M. Raous,et al.  Multibody contact problem including friction in structure assembly , 1992 .

[20]  C. Cryer The Solution of a Quadratic Programming Problem Using Systematic Overrelaxation , 1971 .

[21]  P. M. deZeeuw,et al.  Multigrid and conjugate gradient methods as convergence acceleration techniques , 1985 .

[22]  J. Mandel A multilevel iterative method for symmetric, positive definite linear complementarity problems , 1984 .