Balancing domain decomposition by constraints associated with subobjects


== Abstract ==

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 <math>C(1 + log(\frac {L}{h}))^2</math>, where <math>C</math> is a constant, and <math>h</math> and <math>L</math> are the characteristic sizes of the mesh and the subobjects, respectively. As <math>L</math> can be chosen almost freely, the condition number can theoretically be as small as <math>O(1)</math>. We will discuss the pros and cons of the preconditioner and its application to heterogeneous problems. Numerical results on supercomputers are provided.

== Full document ==
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