The EMI (Extracellular, Membrane, and Intracellular) model is among the first models for describing the electrical activity of the heart at a cellular level. This model couples the three domains and allows discontinuities of potentials between boundaries as well as particular distributions of ion charges on the cellular membranes. In this talk, we will discuss how this model can reproduce at a cellular scale the ischemic behaviour observed in diseased cardiac tissues. Additionally, we will explore and evaluate various multigrid and multilevel solvers performances in solving these systems, analyzing their efficacy on both CPU and GPU architectures. Joint work with Ngoc Mai Monica Huynh and Simone Scacchi.