  In this work, we are interested in solving large linear systems stemming from
the Extra-Membrane-Intra (EMI) model, which is employed for simulating
excitable tissues at a cellular scale. After setting the related systems of
partial differential equations (PDEs) equipped with proper boundary conditions,
we provide numerical approximation schemes for the EMI PDEs and focus on the
resulting large linear systems. We first give a relatively complete spectral
analysis using tools from the theory of Generalized Locally Toeplitz matrix
sequences. The obtained spectral information is used for designing appropriate
(preconditioned) Krylov solvers. We show, through numerical experiments, that
the presented solution strategy is robust w.r.t. problem and discretization
parameters, efficient and scalable.
