  A simple variant of the BDDC preconditioner in which constraints are imposed
on a selected set of subobjects (subdomain subedges, subfaces and vertices
between pairs of subedges) is presented. We are able to show that the condition
number 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 and
the subobjects, respectively. As $L$ can be chosen almost freely, the condition
number can theoretically be as small as $O(1)$. We will discuss the pros and
cons of the preconditioner and its application to heterogeneous problems.
Numerical results on supercomputers are provided.
