Boris-SDC: A high order generalisation of the Boris integrator

The Boris integrator is a very widely employed numerical method for solving the Lorentz equations. It is used very successfully and is cheap and quite accurate. However, being essentially a Verlet-type method, it is intrinsically limited to second order accuracy. In the talk I will present Boris-SDC, a high-order generalization based on spectral deferred corrections (SDC). SDC can be interpreted as a preconditioned Richardson iteration to solve for the stages of a collocation method and the Boris integrator can be used as a base method or preconditioner. Properties of the new method will be analysed for single and multiple particle examples. I will also comment on possible strategies to incorporate Boris-SDC into the parallel full approximation scheme in space and time (PFASST).