Implementation of an implicit shear Alfvén operator in the M3D code Original Research Article

A new pair of linear operators is introduced into the partially implicit but largely explicit time advance algorithm for the MHD equations in the M3D code. These operators jointly render the algorithm implicit with respect to propagation of the shear Alfvén wave to leading order. As a result, the maximum stable time step is increased by up to a factor of three for many practical applications. The additional computational cost is trivial for the linear mode of operation and adds only approximately 30% additional execution time per step for nonlinear calculations.