Deflation, projector preconditioning, and balancing in iterative substructuring methods: Connections and new results (Q2882796)

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.