Deflation of conjugate gradients with applications to boundary value problems
SIAM Journal on Numerical Analysis
Preconditioned conjugate gradients for solving singular systems
Journal of Computational and Applied Mathematics - Special issue on iterative methods for the solution of linear systems
A Domain Decomposition Method with Lagrange Multipliers and Inexact Solvers for Linear Elasticity
SIAM Journal on Scientific Computing
SIAM Journal on Numerical Analysis
Dual-Primal FETI Methods for Three-Dimensional Elliptic Problems with Heterogeneous Coefficients
SIAM Journal on Numerical Analysis
A Preconditioner for Substructuring Based on Constrained Energy Minimization
SIAM Journal on Scientific Computing
A Comparison of Deflation and Coarse Grid Correction Applied to Porous Media Flow
SIAM Journal on Numerical Analysis
A Comparison of Deflation and the Balancing Preconditioner
SIAM Journal on Scientific Computing
SIAM Journal on Scientific Computing
Three-Level BDDC in Three Dimensions
SIAM Journal on Scientific Computing
Optimal Quadratic Programming Algorithms: With Applications to Variational Inequalities
Optimal Quadratic Programming Algorithms: With Applications to Variational Inequalities
An algebraic theory for primal and dual substructuring methods by constraints
Applied Numerical Mathematics - 6th IMACS International symposium on iterative methods in scientific computing
Journal of Computational and Applied Mathematics
A hybrid domain decomposition method and its applications to contact problems
A hybrid domain decomposition method and its applications to contact problems
Mathematics and Computers in Simulation
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In this paper, projector preconditioning, also known as the deflation method, as well as the balancing preconditioner are applied to the dual-primal finite element tearing and interconnecting (FETI-DP) and balancing domain decomposition by constraints (BDDC) methods in order to create a second, independent coarse problem. This may help to extend the parallel scalability of classical FETI-DP and BDDC methods without the use of inexact solvers and may also be used to improve the robustness, e.g., for almost incompressible elasticity problems. Connections of FETI-DP methods applying a transformation of basis using a larger coarse space with a corresponding FETI-DP method using projector preconditioning or balancing are pointed out. It is then shown that the methods have essentially the same spectrum. Numerical results for compressible and almost incompressible linear elasticity are provided. The sensitivity of the projection methods to an inexact computation of the projections is numerically investigated and a different behavior for projector preconditioning and the balancing preconditioner is found.