  A novel theoretical convergence rate estimate for a Balancing Domain
Decomposition by Constraints algorithm is proven for the solution of the
cardiac Bidomain model, describing the propagation of the electric impulse in
the cardiac tissue. The non-linear system arises from a fully implicit time
discretization and a monolithic solution approach. The preconditioned
non-symmetric operator is constructed from the linearized system arising within
the Newton-Krylov approach for the solution of the non-linear problem; we
theoretically analyze and prove a convergence rate bound for the Generalised
Minimal Residual iterations' residual. The theory is confirmed by extensive
parallel numerical tests, widening the class of robust and efficient solvers
for implicit time discretizations of the Bidomain model.
