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

We propose a class of method for the adaptive selection of the coarse space of the BDDC and FETI-DP iterative substructuring methods. The methods work by adding coarse degrees of freedom constructed from eigenvectors associated with intersections of selected pairs of adjacent substructures. It is assumed that the starting coarse degrees of freedom are already sufficient to prevent relative rigid body motions in any selected pair of adjacent substructures. A heuristic indicator of the the condition number is developed and a minimal number of coarse degrees of freedom is added to decrease the indicator under a given threshold. It is shown numerically on 2D elasticity problems that the indicator based on pairs of substructures with common edges predicts the actual condition number reasonably well, and that the method can select adaptively the hard part of the problem and concentrate computational work there to achieve good convergence of the iterations at a modest cost.