#### Duk-Soon Oh, Olof B. Widlund, and Clark R. Dohrmann

#### A BDDC Algorithm for Raviart-Thomas Vector Fields

Abstract:

A BDDC preconditioner is defined by a coarse component, expressed in terms of
primal constraints and a weighted average across the interface between the
subdomains, and
local components given in terms of Schur complements of local subdomain
problems. A BDDC
method for vector field problems discretized with Raviart-Thomas finite
elements is
introduced. Our method is based on a new type of weighted average developed to
deal with
more than one variable coefficient. A bound on the condition number of the
preconditioned
linear system is also provided which
is independent of the values and jumps of the coefficients across the interface
and has a
polylogarithmic condition number bound in terms of the number of degrees of
freedom of the
individual subdomains. Numerical experiments for two and three dimensional
problems are
also presented, which support the theory and show the effectiveness of our
algorithm even
for certain problems not covered by our theory.