An adaptive BDDC method enhanced with prior selected primal constraints

Abstract

An adaptive BDDC (Balancing Domain Decomposition by Constraints) method is considered for three dimensional elliptic problems with coefficients of random variation and high contrast. For such model problems, a certain generalized eigenvalue problem on each subdomain interface is formed to select primal constraints adaptively. In three dimensions, eigenvalue problems are formed on each face or edge nodal equivalence classes. For the case of edges, proposed eigenvalue problems in previous studies are not satisfactory while those for faces perform very effectively. The eigenvalue problems can be enhanced by utilizing prior selected primal constraints. In this paper, this new idea is adopted when forming edge eigenvalue problems and the resulting adaptive BDDC preconditioner is analyzed. In numerical experiments, the new edge eigenvalue problem is also shown to provide a more optimal set of adaptive primal constraints compared to those in the previous studies.