Substructuring preconditioners for the bidomain extracellular potential problem

We study the efficient solution of the linear system arising from the discretization by the mortar method of mathematical models in electrocardiology. We focus on the bidomain extracellular potential problem and on the class of substructuring preconditioners. We verify that the condition number of the preconditioned matrix only grows polylogarithmically with the number of degrees of freedom as predicted by the theory and validated by numerical tests. Moreover, we discuss the role of the conductivity tensors in building the preconditioner.