Balancing Domain Decomposition by Constraints (BDDC) and Finite Element Tearing
and Interconnecting Dual Primal (FETI-DP) methods are among the most powerful
methods for preconditioning linear systems arising from the finite element
discretization of linear and nonlinear
PDEs. In the last decade they have been successfully applied to many different
bilinear forms, either symmetric or non-symmetric, positive definite or indefinite.
The robustness of the methods has been extensively proved
for scalar and vector-valued elliptic problems, and for a wide range of
discretizations, from low-order finite elements to spectral elements and NURBS based
discretizations arising from IsoGeometric Analysis. For any particular application,
the success of BDDC and FETI-DP algorithms depends on the choice of an averaging
operator and of a set of so-called primal continuity constraints.

PETSc is a widely used suite of data structures and routines for the scalable solution
of scientific applications modeled by PDEs. It is an object oriented library written in
C and parallelized with MPI which can exploit different backends for matrix and vector
operations such as shared memory parallelism on the CPU (using pthreads or OpenMP),
NVIDIA GPUs (with CUDA) and Xeon Phi co-processors (via OpenCL).

In this talk we will briefly introduce the BDDC and FETI-DP methods with an emphasis
on algorithmic aspects. The current implementation of the methods, provided to
the PETSc library by the corresponding author, will be presented, together with
available
user customizations. Current developments for the new deluxe scaling operator and
the adaptive choice of constraints will be also discussed. Experimental results will
be provided for the Cardiac Bidomain model discretized with low-order finite
elements, and for scalar elliptic problems discretized with NURBS. Also, recent
results on H(curl) problems discretized with lowest order Nedelec elements will be
discussed.