LAUSR

We study preconditioned iterative methods for the linear system arising in the numerical discretization of the Bidomain equations in electrocardiology. In each step of the time integration, a block two-by-two linear system is obtained and needed to be solved numerically. A preconditioning strategy based on an alternating splitting of the coefficient matrix is proposed to solve such linear systems. The method is a two-parameter modification of the splitting method recently introduced by Chen et al. (J Comput Appl Math 321:487–498, 2017). Theoretically, we demonstrate that the spectrum of the resulting preconditioned matrix shows a tight cluster at unity. The analytic values of the sub-optimal iteration parameters are established and numerical experiments are presented to illustrate the effectiveness of this approach.