SIAM Journal on Scientific and Statistical Computing
Fast iterative solution of stabilised Stokes systems part II: using general block preconditioners
SIAM Journal on Numerical Analysis
Software for simplified Lanczos and QMR algorithms
Applied Numerical Mathematics - Special issue on iterative methods for linear equations
A Sparse Approximate Inverse Preconditioner for the Conjugate Gradient Method
SIAM Journal on Scientific Computing
A comparative study of sparse approximate inverse preconditioners
IMACS'97 Proceedings on the on Iterative methods and preconditioners
Constraint Preconditioning for Indefinite Linear Systems
SIAM Journal on Matrix Analysis and Applications
Efficient preconditioning of the linearized Navier—Stokes equations for incompressible flow
Journal of Computational and Applied Mathematics - Special issue on numerical analysis 2000 Vol. VII: partial differential equations
Robust Approximate Inverse Preconditioning for the Conjugate Gradient Method
SIAM Journal on Scientific Computing
Krylov Subspace Methods for Saddle Point Problems with Indefinite Preconditioning
SIAM Journal on Matrix Analysis and Applications
Preconditioning Indefinite Systems in Interior Point Methods for Optimization
Computational Optimization and Applications
Block triangular preconditioners for symmetric saddle-point problems
Applied Numerical Mathematics - Numerical algorithms, parallelism and applications
Implicit-Factorization Preconditioning and Iterative Solvers for Regularized Saddle-Point Systems
SIAM Journal on Matrix Analysis and Applications
Inexact constraint preconditioners for linear systems arising in interior point methods
Computational Optimization and Applications
Constraint-Style Preconditioners for Regularized Saddle Point Problems
SIAM Journal on Matrix Analysis and Applications
A fully coupled 3-D mixed finite element model of Biot consolidation
Journal of Computational Physics
Journal of Computational and Applied Mathematics
Parallel inexact constraint preconditioners for saddle point problems
Euro-Par'11 Proceedings of the 17th international conference on Parallel processing - Volume Part II
Hi-index | 31.45 |
The Finite Element (FE) integration of the coupled consolidation equations requires the solution of linear symmetric systems with an indefinite saddle point coefficient matrix. Because of ill-conditioning, the repeated solution in time of the FE equations may be a major computational issue requiring ad hoc preconditioning strategies to guarantee the efficient convergence of Krylov subspace methods. In the present paper a Mixed Constraint Preconditioner (MCP) is developed combining implicit and explicit approximations of the inverse of the structural sub-matrix, with the performance investigated in some representative examples. An upper bound of the eigenvalue distance from unity is theoretically provided in order to give practical indications on how to improve the preconditioner. The MCP is efficiently implemented into a Krylov subspace method with the performance obtained in 2D and 3D examples compared to that of Inexact Constraint Preconditioners and Least Square Logarithm scaled ILUT preconditioners. Two variants of MCP (T-MCP and D-MCP), developed with the aim at reducing the cost of the preconditioner application, are also tested. The results show that the MCP variants constitute a reliable and robust approach for the efficient solution of realistic coupled consolidation FE models, and especially so in severely ill-conditioned problems.