This paper proposes a hybrid frequency-time integral-equation method for the time-domain wave equation in both two- and three-dimensional spatial domains. The method proceeds via Fourier transformation in time and by means of solution of a fixed number of frequency-domain integral equations it can compute time-domain solutions for arbitrarily long times with superalgebraically small errors. The approach relies on two main enabling elements: 1) a smooth time-windowing methodology to enable computation for incident wave packets of long duration, and 2) a novel Fourier transform approach which, without requiring zero-padding or time-tracking for solution validity, delivers spectral accuracy, without dispersion, in a time-parallel manner by synthesizing in an efficient manner frequency-domain solutions with superior accuracy obtained by well-understood classical methods. Recognizing the natural generalization of the ideas to Maxwell's equations, and indeed any linear equation, in conjunction with appropriate integral equation solvers which can readily handle complex structures with significant advantages over volumetric methods as well as material dispersion and complex interface conditions, the overall method is an advantageous new approach to enable advances in understanding scattering of ultrawideband signals with diverse scientific applications.
