  In silico models of cardiac electromechanics couple together mathematical
models describing different physics. One instance is represented by the model
describing the generation of active force, coupled with the one of tissue
mechanics. For the numerical solution of the coupled model, partitioned
schemes, that foresee the sequential solution of the two subproblems, are often
used. However, this approach may be unstable. For this reason, the coupled
model is commonly solved as a unique system using Newton type algorithms, at
the price, however, of high computational costs. In light of this motivation,
in this paper we propose a new numerical scheme, that is numerically stable and
accurate, yet within a fully partitioned (i.e. segregated) framework.
Specifically, we introduce, with respect to standard segregated scheme, a
numerically consistent stabilization term, capable of removing the nonphysical
oscillations otherwise present in the numerical solution of the commonly used
segregated scheme. Our new method is derived moving from a physics-based
analysis on the microscale energetics of the force generation dynamics. By
considering a model problem of active mechanics we prove that the proposed
scheme is unconditionally absolutely stable (i.e. it is stable for any time
step size), unlike the standard segregated scheme, and we also provide an
interpretation of the scheme as a fractional step method. We show, by means of
several numerical tests, that the proposed stabilization term successfully
removes the nonphysical numerical oscillations characterizing the non
stabilized segregated scheme solution. Our numerical tests are carried out for
several force generation models available in the literature, namely the
Niederer-Hunter-Smith model, the model by Land and coworkers, and the
mean-field force generation model that we have recently proposed. Finally, we
apply the proposed scheme [...]
