High-order Runge-Kutta multiresolution time-domain methods for computational electromagnetics

In this paper we introduce a class of Runge-Kutta multiresolution time-domain (RK-MRTD) methods for problems of electromagnetic wave propagation that can attain an arbitrarily high order of convergence in both space and time. The methods capitalize on the high-order nature of spatial multiresolution approximations by incorporating time integrators with convergence properties that are commensurate with these. More precisely, the classical MRTD approach is adapted here to incorporate mth-order m-stage low-storage Runge-Kutta methods for the time integration. As we show, if compactly supported wavelets of order N are used (e.g., the Daubechies D-N functions) and m = N, then the RK-MRTD methods deliver solutions that converge with this overall order; a variety of examples illustrate these properties. Moreover, we further show that the resulting algorithms are well suited to parallel implementations, as we present results that demonstrate their near-optimal scaling.