A Stabilized Time-Domain Combined Field Integral Equation Using the Quasi-Helmholtz Projectors

This article introduces a time-domain combined field integral equation (TD-CFIE) for electromagnetic scattering by a perfect electric conductor (PEC). The new equation is obtained by leveraging the quasi-Helmholtz projectors, which separate both the unknown and the source fields into solenoidal and irrotational components. These two components are then appropriately rescaled to cure the solution from a loss of accuracy occurring when the time step is large. Yukawa-type integral operators of a purely imaginary wavenumber are also used as a Calderón preconditioner to eliminate the ill-conditioning of matrix systems. The stabilized time-domain electric and magnetic field integral equations are linearly combined in a Calderón-like fashion, then temporally discretized using an appropriate pair of trial functions, resulting in a marching-on-in-time (MOT) linear system. The novel formulation is immune to spurious resonances, dense discretization breakdown, large-time step breakdown, and dc instabilities stemming from non-trivial kernels. Numerical results for both simply-connected and multiply-connected scatterers corroborate the theoretical analysis.