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A simple variant of the BDDC preconditioner in which constraints are imposedon a selected set of subobjects (subdomain subedges, subfaces and verticesbetween pairs of subedges) is presented. We are able to show that the conditionnumber of the preconditioner is bounded by $C \big(1+\log (L/h)\big)^2$, where$C$ is a constant, and $h$ and $L$ are the characteristic sizes of the mesh andthe subobjects, respectively. As $L$ can be chosen almost freely, the conditionnumber can theoretically be as small as $O(1)$. We will discuss the pros andcons of the preconditioner and its application to heterogeneous problems.Numerical results on supercomputers are provided.

Balancing domain decomposition by constraints associated with subobjects