Electromagnetic scattering from 3-D curved dielectric bodies using time-domain integral equations

A boundary integral equation (BIE) approach is developed to calculate transient scattering from dielectric bodies. The treatment is directly in terms of the E and a fields rather than magnetic and electric currents. It employs curvilinear (quadratic) modeling, which allows accurate representation of arbitrarily shaped curved bodies. The treatment is isoparametric with the same quadratic representation of the spatial field variation and with the temporal variation modeled by similar quadratic elements. Integration employs high-order Gaussian quadrature with special treatment of the singular and hypersingular integrals that arise. The treatment is implicit, requiring the solution of a sparse matrix equation at each timestep. This adds only trivially to the cost at each timestep and, by freeing the timestep from the constraint that it be smaller than the smallest nodal spacing, can greatly reduce the number of timesteps that must be employed. Additionally, it produces stable results without resort to the averaging processes proposed elsewhere. Example calculations of scattering from a sphere, a cube, and an almond are presented and compared with earlier published transient results and with results from a frequency domain treatment. Good agreement and improved accuracy is found.