Preconditioned iteration for saddle-point systems with bound constraints arising in contact problems

[1]  M. Fortin,et al.  An efficient hierarchical preconditioner for quadratic discretizations of finite element problems , 2011, Numer. Linear Algebra Appl..

[2]  Michel Fortin,et al.  Iterative solvers for 3D linear and nonlinear elasticity problems: Displacement and mixed formulations , 2010 .

[3]  Daniel Loghin,et al.  Discrete Interpolation Norms with Applications , 2009, SIAM J. Numer. Anal..

[4]  R. Guenette,et al.  Efficient preconditioning techniques for finite‐element quadratic discretization arising from linearized incompressible Navier–Stokes equations , 2009 .

[5]  M. Schäfer,et al.  A fast and robust iterative solver for nonlinear contact problems using a primal‐dual active set strategy and algebraic multigrid , 2007 .

[6]  Mark F. Adams,et al.  Algebraic Multigrid Methods for Direct Frequency Response Analyses in Solid Mechanics , 2007 .

[7]  R.D. Falgout,et al.  An Introduction to Algebraic Multigrid Computing , 2006, Computing in Science & Engineering.

[8]  Yvan Notay,et al.  Aggregation-Based Algebraic Multilevel Preconditioning , 2005, SIAM J. Matrix Anal. Appl..

[9]  Barbara Wohlmuth,et al.  A primal–dual active set strategy for non-linear multibody contact problems , 2005 .

[10]  Yvan Notay,et al.  Algebraic multigrid and algebraic multilevel methods: a theoretical comparison , 2005, Numer. Linear Algebra Appl..

[11]  Pierre Alart,et al.  Conjugate gradient type algorithms for frictional multi-contact problems: applications to granular materials , 2005 .

[12]  Gene H. Golub,et al.  Numerical solution of saddle point problems , 2005, Acta Numerica.

[13]  Yousef Saad,et al.  Iterative methods for sparse linear systems , 2003 .

[14]  David Horák,et al.  Scalability and FETI based algorithm for large discretized variational inequalities , 2003, Math. Comput. Simul..

[15]  Asen Asenov,et al.  Excessive Over-Relaxation Method for Multigrid Poisson Solvers , 2002 .

[16]  Kazufumi Ito,et al.  The Primal-Dual Active Set Strategy as a Semismooth Newton Method , 2002, SIAM J. Optim..

[17]  R. Kornhuber,et al.  Adaptive multigrid methods for Signorini’s problem in linear elasticity , 2001 .

[18]  Cornelis Vuik,et al.  A parallel block-preconditioned GCR method for incompressible flow problems , 2001, Future Gener. Comput. Syst..

[19]  D. Rixen,et al.  FETI‐DP: a dual–primal unified FETI method—part I: A faster alternative to the two‐level FETI method , 2001 .

[20]  Rolf Krause,et al.  Monotone Multigrid Methods for Signorini's Problem with Friction , 2001 .

[21]  Z. Dostál,et al.  Solution of contact problems by FETI domain decomposition with natural coarse space projections , 2000 .

[22]  Mark F. Adams,et al.  Evaluation of three unstructured multigrid methods on 3D finite element problems in solid mechanics , 2000 .

[23]  R. Fletcher,et al.  Practical Methods of Optimization: Fletcher/Practical Methods of Optimization , 2000 .

[24]  Gene H. Golub,et al.  A Note on Preconditioning for Indefinite Linear Systems , 1999, SIAM J. Sci. Comput..

[25]  Patrick R. Amestoy,et al.  Multifrontal parallel distributed symmetric and unsymmetric solvers , 2000 .

[26]  Axel Klawonn,et al.  Block-Triangular Preconditioners for Saddle Point Problems with a Penalty Term , 1998, SIAM J. Sci. Comput..

[27]  Zdeněk Dostál,et al.  Solution of Coercive and Semicoercive Contact Problems by FETI Domain Decomposition , 1998 .

[28]  R. D. Wood,et al.  Nonlinear Continuum Mechanics for Finite Element Analysis , 1997 .

[29]  Jinchao Xu,et al.  Preconditioning the Poincaré-Steklov operator by using Green's function , 1997, Math. Comput..

[30]  Homer F. Walker,et al.  Choosing the Forcing Terms in an Inexact Newton Method , 1996, SIAM J. Sci. Comput..

[31]  C. Vuik.  New insights in GMRES-like methods with variable preconditioners , 1995 .

[32]  G. Schmidt.  Boundary element discretization of Poincar\'e--Steklov operators , 1994 .

[33]  Cornelis Vuik,et al.  GMRESR: a family of nested GMRES methods , 1994, Numer. Linear Algebra Appl..

[34]  Rüdiger Verfürth,et al.  A posteriori error estimation and adaptive mesh-refinement techniques , 1994 .

[35]  William Gropp,et al.  Newton-Krylov-Schwarz Methods in CFD , 1994 .

[36]  Yousef Saad,et al.  Hybrid Krylov Methods for Nonlinear Systems of Equations , 1990, SIAM J. Sci. Comput..

[37]  R. Fletcher.  Practical Methods of Optimization , 1988 .

[38]  D. Trystram,et al.  A Conjugate projected gradient method with preconditioning for unilateral contact problems , 1988 .

[39]  M. Delfour,et al.  Shapes and Geometries: Analysis, Differential Calculus, and Optimization , 1987 .

[40]  H.-O. May,et al.  The conjugate gradient method for unilateral problems , 1986 .

[41]  Anil Chaudhary,et al.  A SOLUTION METHOD FOR PLANAR AND AXISYMMETRIC CONTACT PROBLEMS , 1985 .

[42]  S. Eisenstat,et al.  Variational Iterative Methods for Nonsymmetric Systems of Linear Equations , 1983 .

[43]  B. Torstenfelt,et al.  Contact problems with friction in general purpose finite element computer programs , 1983 .

[44]  M. Fortin,et al.  Augmented Lagrangian methods : applications to the numerical solution of boundary-value problems , 1983 .

[45]  R. Dembo,et al.  INEXACT NEWTON METHODS , 1982 .

[46]  Nguyen Dang Hung,et al.  Frictionless contact of elastic bodies by finite element method and mathematical programming technique , 1980 .