An accurate broadband method of moments using higher order basis functions and tree-loop decomposition

The method of moments (MoM) has been one of the most popular computational methods for the solution of electromagnetic scattering problems. While many MoM formulations are possible, the electric field integral equation (EFIE) formulation is of great importance as it can be applied to either closed or open structures. Unfortunately, at very low frequencies, naive EFIE implementations become inaccurate due to severe cancellation in the computation of the scalar potential. This work presents a method to create a loop-tree decomposition for the divergence-conforming higher-order triangular patch bases so that a single mesh can be used to gather broadband information. The proposed method is completely general, and works for any basis function order. In addition, frequency scaling of the impedance matrix was used to further lower its condition number and the right hand side was reformulated to alleviate subtractive cancellation.