A DC-Stable, Well-Balanced, Calderón Preconditioned Time Domain Electric Field Integral Equation

The marching-on-in-time (MOT) solution of the time domain electric field integral equation (TD-EFIE) has traditionally suffered from a number of problems, including: 1) instability; 2) spurious static contributions plaguing the solution; 3) low-frequency breakdown; and 4) dense discretization breakdown. The first issue can be resolved by employing proper space-time Galerkin discretization schemes and accurate quadrature methods. The second and the third issue have been resolved by the quasi-Helmholtz Projected TD-EFIE (qHP-TDEFIE). This contribution introduces a multiplicative preconditioner which can be applied to the qHP-TDEFIE, without further modifying the original scheme. This preconditioner is based on Calderón techniques and guarantees that the MOT system can be solved efficiently using iterative methods, not only for large time step sizes but also for dense spatial discretizations, and for both simply and multiply connected geometries.