The solution of nonlinear problems, eg, in material science, requires fast and highly scalable
parallel solvers. Finite element tearing and interconnecting dual primal (FETI-DP) domain …

Abstract The Balancing Domain Decomposition by Constraints (BDDC) method is the most
advanced method from the Balancing family of iterative substructuring methods for the …

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 …

The BDDC method [2] is one of the most advanced methods of iterative substructuring. In the
case of many substructures, solving the coarse problem exactly becomes a bottleneck …

A BDDC (balancing domain decomposition by constraints) method is developed for elliptic
equations, with discontinuous coefficients, discretized by mortar finite element methods for …

BDDC algorithms have previously been extended to the saddle point problems arising from
mixed formulations of elliptic and incompressible Stokes problems. In these two-level BDDC …

Convergence of domain decomposition methods rely heavily on the efficiency of the coarse
space used in the second level. The GenEO coarse space has been shown to lead to a …

A new nonlinear version of the well-known FETI-DP method (Finite Element Tearing and
Interconnecting Dual-Primal) is introduced. In this method, the nonlinear problem is …

Abstract The Virtual Element Method (VEM) is a novel family of numerical methods for
approximating partial differential equations on general polygonal or polyhedral …

Aerodynamic flows involve features with a wide range of spatial and temporal scales which
need to be resolved in order to accurately predict desired engineering quantities. While …