Time domain Calderón identities and their application to the integral equation analysis of scattering by PEC objects, part I: preconditioning

Time domain electric field integral equations often are used to analyze transient scattering from perfect electrically conducting objects. When discretized using marching-on-in-time recipes they give rise to linear systems of equations that can be solved for the induced currents for all time steps. Unfortunately, when the scatterer is approximated by increasingly dense meshes, the condition number of these systems grows rapidly, slowing down the convergence of iterative solvers. Here, time domain Calderon identities are derived and subsequently used to construct a Calderon-preconditioned time domain electric field integral equation that can be discretized even with dense meshes using Buffa-Christiansen basis functions. Numerical results that demonstrate the effectiveness and accuracy of the proposed method are presented