## 2 Method of Moments of Electromagnetic Field  
According to the boundary condition, the magnetic field integral equation (MFIE) and electric field integral equation (EFIE) are established as:  
\[\overset{\rightarrow}{E}(\overset{\rightarrow}{r})|_{\text{tan}}=j\omega\mu \int_{S}[\overset{\rightarrow}{\int}_{S}(\overset{\rightarrow}{r}^{\prime})+ \frac{1}{k^{2}}\
abla(\
abla^{\prime}\overset{\rightarrow}{f}_{S})]G( \overset{\rightarrow}{r},\overset{\rightarrow}{r}^{\prime})d\overset{ \rightarrow}{r}^{\prime}|_{\text{tan}} \tag{1}\]  
\[\hat{n}\times\overset{\rightarrow}{H}=\frac{\overset{\rightarrow}{\int}_{S} (\overset{\rightarrow}{r}^{\prime})}{2}-\hat{n}\times P.V.\int_{S}\overset{ \rightarrow}{f}_{S}(\overset{\rightarrow}{r}^{\prime})\times\
abla G( \overset{\rightarrow}{r},\overset{\rightarrow}{r}^{\prime})d\overset{ \rightarrow}{r}^{\prime} \tag{2}\]  
where \(P.V.\) is Cauchy Principal value integral in Equation (2) \(k\) and \(\eta\) are wave number and wave impedance, \(G(\overset{\rightarrow}{r},\overset{\rightarrow}{r}^{\prime})\) is [PERSON]'s function in the free space. \(\overset{\rightarrow}{\int}_{S}\) represent current densities on surface.  
In order to solve Equations (1) and (2), triangular patches are used to discrete the surface. The RWG basis functions [1] are defined on triangular patches. Hence the current vector \(I\) can be expressed into  
\[I\approx\sum_{n=1}^{N}I_{n}\overset{\rightarrow}{\int}_{I}\left(\overset{ \rightarrow}{r}\right) \tag{3}\]  
where \(\overset{\rightarrow}{\int}_{I}\left(\overset{\rightarrow}{r}\right)\) and \(N\) are the basis function and the number of unknowns, respectively. \(I_{n}\) is current coefficient vector. The following conclusions can be drawn from the Galerkin test:  
\[\begin{array}{l}\sum\limits_{n=1}^{N}Z_{1n}I_{n}=V_{1},\\ \ldots\\ \sum\limits_{n=1}^{N}Z_{Nn}I_{n}=V_{N},\end{array} \tag{4}\]  
where \(Z_{mn},(m=1,2,\cdots,N)\) means impedance matrix. \(V_{m}\) is excitation vector. The specific form of \(Z_{mn}\) is as follows  
\[Z_{mn}^{EFIE}=jk\eta\int_{S_{m}}ds\overset{\rightarrow}{f}_{m}\left(\overset{ \rightarrow}{r}\right)\cdot\int_{S_{m}}G\left(\overset{\rightarrow}{r}, \overset{\rightarrow}{r}^{\prime}\right)\overset{\rightarrow}{f}_{n}\left( \overset{\rightarrow}{r}^{\prime}\right)ds^{\prime}-j\frac{\eta}{k}\int_{S_{ m}}ds\left[\
abla\cdot\overset{\rightarrow}{f}_{m}\left(\overset{ \rightarrow}{r}\right)\right]\cdot\int_{S_{n}}G\left(\overset{\rightarrow}{r},\overset{\rightarrow}{r}^{\prime}\right)\left[\
abla\cdot\overset{ \rightarrow}{f}_{n}\left(\overset{\rightarrow}{r}^{\prime}\right)\right]ds^{\prime} \tag{5}\]  
\[Z_{mn}^{MFIE}=\frac{1}{2}\int_{S_{m}}\overset{\rightarrow}{f}_{m}\left( \overset{\rightarrow}{r}\right)\cdot\overset{\rightarrow}{f}_{n}\left( \overset{\rightarrow}{r}\right)ds+\int_{S_{m}}ds\left[\hat{n}\times \overset{\rightarrow}{f}_{m}\left(\overset{\rightarrow}{r}\right)\right] \cdot\int_{S_{n}}\
abla G\left(\overset{\rightarrow}{r},\overset{ \rightarrow}{r}^{\prime}\right)\times\overset{\rightarrow}{f}_{n}\left( \overset{\rightarrow}{r}^{\prime}\right)ds^{\prime} \tag{6}\]  
where, \(\overset{\rightarrow}{f}_{m}\left(\overset{\rightarrow}{r}\right)\) indicate the testing functions. \(S_{m}\) and \(S_{n}\) are their support sets.