  The Time Domain-Electric Field Integral Equation (TD-EFIE) and its
differentiated version are widely used to simulate the transient scattering of
a time dependent electromagnetic field by a Perfect Electrical Conductor (PEC).
The time discretization of the TD-EFIE can be achieved by a space-time Galerkin
approach or, as it is considered in this contribution, by a convolution
quadrature using Implicit Runge-Kutta methods. The solution is then computed
using the Marching-On-in-Time (MOT) algorithm. The differentiated TD-EFIE has
two problems: (i) the system matrix suffers from ill-conditioning when the time
step increases (low frequency breakdown) and (ii) it suffers from the DC
instability, i.e. the formulation allows for the existence of spurious
solenoidal currents that grow slowly in the solution. In this work, we show
that (i) and (ii) can be alleviated by leveraging quasi-Helmholtz projectors to
separate the Helmholtz components of the induced current and rescale them
independently. The efficacy of the approach is demonstrated by numerical
examples including benchmarks and real life applications.
