Public Reporting burden for this collection of information is estimated to average 1 hour per response, including the time for reviewing instructions, searching existing data sources, gathering and maintaining the data needed, and completing and reviewing the collection of information. In recent years, a variety of computational schemes have been developed that accelerate the iterative solution of the dense matrix equations that arise upon discretizing boundary integral equations pertinent to the description of electromagnetic scattering problems. These schemes largely fall into two categories: (i) fast multipole methods and (ii) wavelet/multiresolution schemes. The overall goal of this project is to develop and catalogue all practical hybrids between fast multipole solvers and multiresolution schemes useful to the analysis of electromagnetic boundary value problems. To this end, we developed (i) hybrid plane wave time domain (PWTD) -multiresolution schemes pertinent to the construction of PWTD schemes for lossy media, (ii) PWTD schemes for 2D environments, (iii) PWTD solvers for microstrip structures, (iv) PWTD schemes for low-frequency solvers, (v) PWTD schemes for quasi-planar environments, (vi) PWTD schemes for periodic kernels, (vii) Time-Domain Adaptive Integral (TD-AIM) kernels for solving timedomain integral equations, (viii) TD-AIM accelerated hybrid time domain integral equation -SPICE based circuit solvers, and (ix) a novel multigrid accelerator for the full wave finite element analysis of electromagnetic phenomena. Each and every of these solvers uses a multiresolution framework, either in space, time, or space-time to accelerate a boundary integral or finite element solver pertinent to the analysis of electromagnetic radiation, scattering, or guidance problems beyond what is possible using vanilla fastmultipole methods.