Conforming Discretization Based on Characteristic Basis Function for Magnetic Field Integral Equation

The dual testing scheme using the Buffa–Christiansen (BC) basis function not only maintains the good convergence of the magnetic field integral equation (MFIE) but also improves its accuracy. However, in practical applications, fewer unknowns are desired to reduce the computing resources of the nBC-tested MFIE. In this letter, a novel conforming discretization based on characteristic basis functions (CBFs) is proposed to mitigate the problem of the conventional nBC-tested MFIE. The proposed discretization can acquire a well-conditioned discretization of the identity operator leading to a satisfactory iterative convergence while keeping a conforming testing scheme. The resulting system matrix is smaller than the original system matrix of the conventional nBC-tested MFIE while inheriting satisfactory iterative convergence and accuracy. Numerical results are shown to demonstrate the performance of the proposed method.