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

This paper introduces a time-domain combined field integral equation for electromagnetic scattering by a perfect electric conductor.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 wave number 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 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.