Application of Loop-Flower Basis Functions in the Time-Domain Electric Field Integral Equation

The loop-flower basis functions are applied to get a low-frequency stable time-domain electric field integral equation (TD-EFIE). The quasi-Helmholtz decomposition is performed by the loop-flower basis functions, which are all defined based on mesh nodes. To get a well-posed equation, a temporally differentiated form of the TD-EFIE is tested with the flower function and the undifferentiated form is tested with the loop function. For a robust MOT solver, the averaging scheme is also adopted to alleviate the high-frequency instabilities. Numerical verifications of perfect electric conductor (PEC) transient scattering problems are provided to demonstrate the accuracy and stability of the proposed technique.