  We combine the adaptive and multilevel approaches to the BDDC and formulate a
method which allows an adaptive selection of constraints on each decomposition
level. We also present a strategy for the solution of local eigenvalue problems
in the adaptive algorithm using the LOBPCG method with a preconditioner based
on standard components of the BDDC. The effectiveness of the method is
illustrated on several engineering problems. It appears that the
Adaptive-Multilevel BDDC algorithm is able to effectively detect troublesome
parts on each decomposition level and improve convergence of the method. The
developed open-source parallel implementation shows a good scalability as well
as applicability to very large problems and core counts.
