  We present a new explicit local space-time adaptive framework to decrease the
time required for monodomain simulations for cardiac electrophysiology. Based
on the localized structure of the steep activation wavefront in solutions to
monodomain problems, the proposed framework adopts small time steps and a
tree-based adaptive mesh refinement scheme only in the regions necessary to
resolve these localized structures. The time step and mesh adaptation selection
process is fully controlled by a combination of local error indicators. The
main contributions of this work consist in the introduction of a primal
symmetric interior penalty formulation of the monodomain model and an efficient
algorithmic strategy to manage local time stepping for its temporal
discretization. In a first serial implementation of this framework, we report
decreases in wall-clock time between 2 and 20 times with respect to an
optimized implementation of a commonly used numerical scheme, showing that this
framework is a promising candidate to accelerate monodomain simulations of
cardiac electrophysiology.
