An efficient scattering algorithm for smooth and sharp surfaces: Coiflet-based scalar MFIE

We present a scattering algorithm using the magnetic-field integral equation (MFIE). The MFIE is a second kind integral equation and is well posed, rendering good condition number and fast convergence of the iteration solver. Nonetheless, the MFIE is derived assuming smooth surface, while the RWG discretizes a smooth curved surface into triangular facets with nonsmooth edges. This inconsistency greatly degrades the MFIE performance. In contrast, Coiflets are highly regular and completely differentiable. As a high-order function, the Coiflet basis conforms to the geometry in expansion, and it is dually used in conformal testing, preserving all merits of the MFIE. Due to its high-precision one-point quadrature (OPQ), the Coiflet algorithm results in O(N) for smooth surfaces up to 1800 λ² and begins trend of O(N log N) when surface increases to 3200 λ². Numerical results are compared with the RWG-MLFMA-based commercial software, FEKO, and the Mie theory. Good agreement has been observed.