Solution of the Electric Field Integral Equation When It Breaks Down

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With a method developed in this work, we find the solution of the original electric field integral equation (EFIE) at an arbitrary frequency where the EFIE breaks down due to low frequencies and/or dense discretizations. This solution is equally rigorous at frequencies where the EFIE does not break down and is independent of the basis functions used. We also demonstrate, both theoretically and numerically, the fact that although the problem is commonly termed low-frequency breakdown, the solution at the EFIE breakdown can be dominated by fullwave effects instead of just static or quasi-static physics. The accuracy and efficiency of the proposed method is demonstrated by numerical experiments involving inductance, capacitance, RCS extraction, and a multiscale example with a seven-orders-of-magnitude ratio in geometrical scales, at all breakdown frequencies of an EFIE. In addition to the EFIE, the proposed method is also applicable to other integral equations and numerical methods for solving Maxwell's equations.