A space-time polar quadrature technique for numerical integration of Green's function interactions in time-domain integral equations is presented. The method transforms 2-D surface space-time integrals associated with vector and scalar potentials to a 1-D integral that is performed using Gauss-Legendre integration. The advantage of the presented technique compared to standard 2-D Gaussian quadrature is that time delays between each section of the source basis function and the observation point are accounted for exactly in an analytic manner. This ensures highly accurate temporal behavior of the Green's function interactions thereby contributing to the stability of the overall time-domain integral equations.

We present a computational study of signal propagation and attenuation of a 200 MHz planar loop antenna in a cave environment. The cave is modeled as a straight and lossy random rough wall. To simulate a broad frequency band, the full wave Maxwell equations are solved directly in the time domain via a high order vector finite element discretization using the massively parallel CEM code EMSolve. The numerical technique is first verified against theoretical results for a planar loop antenna in a smooth lossy cave. The simulation is then performed for a series of random rough surface meshes in order to generate statistical data for the propagation and attenuation properties of the antenna in a cave environment. Results for the mean and variance of the power spectral density of the electric field are presented and discussed.

This report summarizes the work performed for Lawrence Livermore National Laboratory (LLNL) at the University of Washington between September 2004 and May 2006. This project studied fast solvers and stability for time domain integral equations (TDIE), especially as applied to radiating boundary for a massively parallel FEM solver.

Index Terms-time domain, integral equations, hybrid formulation, finite element method, method of moments.

We present a computational study of signal propagation and attenuation of a 200 MHz dipole antenna in a cave environment. The cave is modeled as a straight and lossy random rough wall. To simulate a broad frequency band, the full wave Maxwell equations are solved directly in the time domain via a high order vector finite element discretization using the massively parallel CEM code EMSolve. The simulation is performed for a series of random meshes in order to generate statistical data for the propagation and attenuation properties of the cave environment. Results for the power spectral density and phase of the electric field vector components are presented and discussed.