A comparison of multilevel solvers for the cardiac bidomain equations

Computing the extracellular potentials in a bidomain cardiac activation model is a computationally significant step in the solution process. Thus, using a fast solver can drastically reduce the overall time of simulation. Solving for the extracellular potentials involves inverting the matrix coming from the elliptic equation describing the extracellular-intracellular potential coupling. Elliptic equations are known to yield matrices that become progressively more ill-conditioned as the spatial resolution is increased. However, optimal multilevel solution methods are known to exist for these equations given enough effort is placed into developing the correct solution components. Two multilevel solvers that automatically perform much of this work are black box multigrid (BOXMG) and algebraic multigrid (AMG). In this paper, we compare the performance of BOXMG and AMG as solvers for the elliptic component of the bidomain equations. Our investigation is with respect to simulations of reentry in two-dimensional cardiac tissue.