New concepts for the Multiresolution Time Domain (MRTD) analysis of microwave structures

The Multiresolution Time Domain (MRTD) technique presents a natural framework for the implementation of spatio-temporal adaptive gridding. This feature can lead to significant reductions in the simulation time for large-scale problems of practical interest to the microwave community. With the exception of the Haar-based MRTD scheme, all the other methods presented in the literature employ high-order finite difference operators for the numerical approximation of the spatial partial derivatives of Maxwell's equations. However, little attention has been devoted to the study of the convergence properties of these schemes, which are typically associated with significantly increased numerical work and stability limits that are small fractions of the FDTD Courant stability limit. In this paper, it is first noted that high-order spatial finite differences still produce second-order error convergence for the method, as long as they are coupled with the second-order accurate leap-frog time integration. This prompts us to investigate other possibilities for the formulation of MRTD schemes, revisiting the choice of the leap-frog scheme for time-integration, with the purpose of improving the convergence properties of MRTD, employing high-order time integrators.