Adaptive Coarse Space Selection in the BDDC and the FETI-DP Iterative Substructuring Methods: Optimal Face Degrees of Freedom

Abstract

We propose adaptive selection of the coarse space of the BDDC and FETI-DP iterative substructuring methods by adding coarse degrees of freedom (dofs) on faces between substructures constructed using eigenvectors associated with the faces. Provably the minimal number of coarse dofs on the faces is added to decrease a heuristic indicator of the condition number under a target value specified a priori. It is assumed that corner dofs are already sufficient to prevent relative rigid body motions of any two substructures with a common face. It is shown numerically on a 2D elasticity problem that the indicator is reasonably close to the actual condition number and that the method can find automatically the hard part of the problem and concentrate the computational work there to achieve the target value for the condition number and good convergence of the iterations, at a modest cost.