A new time domain electric field integral equation is proposed to solve low frequency problems. This new formulation uses the current and charge densities as unknowns, with a form of the continuity equation that is weighted by a Green's function as a second constraining equation. This equation can be derived from a scalar potential equivalence principle integral equation, which is in contrast to the traditional strong form of the continuity equation that has been used in an ad-hoc manner in the augmented EFIE. Numerical results demonstrate the improved stability of this approach, as well as the accuracy at low frequencies.
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