AbstractThe balancing domain decomposition by constraints (BDDC) preconditioner requires direct solutions of two linear systems for each substructure and one linear system for a global coarse problem. The computations and memory needed for these solutions can be prohibitive if any one system is too large. We investigate an approach for addressing this issue based on approximating the direct solutions using preconditioners. In order to retain the attractive numerical properties of the exact version of BDDC, some of the preconditioners must possess a property related to the substructure null spaces. We describe a simple method to equip preconditioners with this property. Numerical results demonstrate the usefulness of the approach and confirm the theory. Published in 2006 by John Wiley & Sons, Ltd.