A simplified 3D plane wave time domain (PWTD) algorithm

This paper presents a novel and simplified three-dimensional (3D) plane wave time domain (PWTD) algorithm. PWTD schemes constitute extensions of frequency domain (Helmholtz equation) fast multipole methods to the time domain (wave equation); as such, they permit the fast evaluation of transient wave fields generated by known, bandlimited sources. Previously, we demonstrated the usefulness of the PWTD scheme in accelerating the solution of time domain integral equations pertinent to the analysis of electromagnetic scattering problems. Implementation of such solvers however is hindered by the relative complexity of the underlying PWTD kernels. The proposed modified kernel is simpler and easier to implement than previously reported kernels. In addition, compared to prior PWTD schemes: (i) the new scheme features a simplified translation operator and relies on uniform spherical sampling of far-field signatures; (ii) requires less memory without sacrificing computational complexity; and (iii) is more easily extended to environments other than free-space.