Splitting a heart

Abstract: This thesis investigates and numerically solves the Wohlfart-Arloch equations describing the electrical activity in the atrial part of the heart. This is done through operator splitting that is allowing the diffusion of ionic currents, and the local voltage-driven reactions in each cell to be de-coupled. The local reactions can be solved in closed form, and the diffusion part is solved with a spectral method by interpolating using eigenmodes. The problem of initiating the system is solved by introducing time-dependent boundary conditions and solving these parts as a series. Systematic investigations are carried out both concerning the numerical errors and also the wave speed, multiple pulse shape, and other characteristics relevant to ascertaining the validity of the numerical method used.