There has recently been a considerable amount of activity in developing adaptive methods for the selection of primal constraints for BDDC algorithms and, in particular, for BDDC deluxe variants.
Much of the earlier work for adaptive BDDC and FETI-DP iterative substructuring algorithms, which has been supported by theory, has been confined to developing primal constraints for equivalence classes related to two subdomain boundaries such as those for the subdomain edges for problems defined on domains in the plane; see, in particular, the paper by Klawonn, Radtke, and Rheinbach .
resulting in a linear system of equations to be solved using BDDC domain decomposition algorithms, in particular, its deluxe variant.
In particular, BDDC researchers are investigating using switchgrass and miscanthus for natural fiber reinforcement.
A group of researchers at the BDDC has been investigating ways to engineer new biocomposites using hybrid bio-resources including grasses, agri-residues, and lignin.
Scalar elliptic problems in the plane are analyzed in [7, 9];  includes a FETI-DP algorithm for scalar elliptic and elasticity problems, and [5, 10] include an iterative substructuring method and a BDDC deluxe algorithm for problems in H(curl) in 2D, respectively.
In addition, a BDDC algorithm with deluxe scaling is considered in  for uniform domains in 2D, and in  for 3D.
Recently, in , new tools are developed for more general subdomains and a BDDC deluxe method, where the faces are assumed to be only star-shaped polygons.
BDDC, domain decomposition, saddle point problem, condition number, hybrid finite element method
In our recent paper , we extended the BDDC algorithm to this mixed formulation of elliptic problems.
BDDC, domain decomposition, saddle point problem, condition number, benign space, edge/face-based iterative substructuring method
The BDDC algorithms, introduced by Dohrmann in , see also [13, 14], are nonoverlapping domain decomposition methods, which are similar to the balancing Neumann-Neumann (BNN) algorithms.