On a Time Domain Calderón Preconditioned CFIE Discretized with Convolution Quadratures

Several standard integral equations in the time domain suffer from at least one of the following limitations: 1) conditioning breakdowns, 2) internal resonances, or 3) DC-instabilities. The standard time domain combined field integral equation (CFIE) being no exception, is plagued by the large time step and dense discretization breakdowns. Calderón preconditioning strategies are commonly proposed to address these issues in the frequency domain but, to this day, they were not available for convolution quadrature CFIEs. This work will fill this gap proposing a new Calderón approach leading to a well-conditioned and resonant-free convolution quadrature discretized equation.