  We study the effect of adaptive mesh refinement on a parallel domain
decomposition solver of a linear system of algebraic equations. These concepts
need to be combined within a parallel adaptive finite element software. A
prototype implementation is presented for this purpose. It uses adaptive mesh
refinement with one level of hanging nodes. Two and three-level versions of the
Balancing Domain Decomposition based on Constraints (BDDC) method are used to
solve the arising system of algebraic equations. The basic concepts are
recalled and components necessary for the combination are studied in detail. Of
particular interest is the effect of disconnected subdomains, a typical output
of the employed mesh partitioning based on space-filling curves, on the
convergence and solution time of the BDDC method. It is demonstrated using a
large set of experiments that while both refined meshes and disconnected
subdomains have a negative effect on the convergence of BDDC, the number of
iterations remains acceptable. In addition, scalability of the three-level BDDC
solver remains good on up to a few thousands of processor cores. The largest
presented problem using adaptive mesh refinement has over 10^9 unknowns and is
solved on 2048 cores.
