  Two novel parallel Newton-Krylov Balancing Domain Decomposition by
Constraints (BDDC) and Dual-Primal Finite Element Tearing and Interconnecting
(FETI-DP) solvers are here constructed, analyzed and tested numerically for
implicit time discretizations of the three-dimensional Bidomain system of
equations.
  This model represents the most advanced mathematical description of the
cardiac bioelectrical activity and it consists of a degenerate system of two
non-linear reaction-diffusion partial differential equations (PDEs), coupled
with a stiff system of ordinary differential equations (ODEs).
  A finite element discretization in space and a segregated implicit
discretization in time, based on decoupling the PDEs from the ODEs, yields at
each time step the solution of a non-linear algebraic system.
  The Jacobian linear system at each Newton iteration is solved by a Krylov
method, accelerated by BDDC or FETI-DP preconditioners, both augmented with the
recently introduced {\em deluxe} scaling of the dual variables.
  A polylogarithmic convergence rate bound is proven for the resulting parallel
Bidomain solvers.
  Extensive numerical experiments on linux clusters up to two thousands
processors confirm the theoretical estimates, showing that the proposed
parallel solvers are scalable and quasi-optimal.
