  The aim of the present work is to design, analyze theoretically, and test
numerically, a generalized Dryja-Smith-Widlund (GDSW) preconditioner for
composite Discontinuous Galerkin discretizations of multicompartment parabolic
reaction-diffusion equations, where the solution can exhibit natural
discontinuities across the domain. We prove that the resulting preconditioned
operator for the solution of the discrete system arising at each time step
converges with a scalable and quasi-optimal upper bound for the condition
number. The GDSW preconditioner is then applied to the EMI (Extracellular -
Membrane - Intracellular) reaction-diffusion system, recently proposed to model
microscopically the spatiotemporal evolution of cardiac bioelectrical
potentials. Numerical tests validate the scalability and quasi-optimality of
the EMI-GDSW preconditioner, and investigate its robustness with respect to the
time step size as well as jumps in the diffusion coefficients.
