The planar integral equations derived earlier can be solved numerically by discretizing the unknown currents using a proper meshing scheme. The original functional equations are reduced to discretized linear algebraic equations over elementary cells. The unknown quantities are found by solving this system of linear equations, and many other parameters can be computed thereafter. This method of numerical solution of integral equations is known as the Method of Moments (MoM). In this method, the unknown electric and magnetic currents are represented by expansions of basis functions as follows:
[[File:PMOM2.png]]<math>J(r) = \sum_{n=1}^N I_n^{(J)} f_n^{(J)} (r)</math>
where '''f:<sub>n</sub><supmath>M(Jr)</sup>''' and '''f<sub>= \sum_{k</sub><sup>=1}^K V_k^{(M)</sup>''' are the generalized vector basis functions for the expansion of electric and magnetic currents, respectively, and I<sub>n</sub><sup>} f_k^{(JM)</sup> and V<sub>k</sub><sup>} (Mr)</supmath> are the unknown amplitudes of these basis functions, which have to be determined<!--[[File:PMOM2. Substituting these expansions into the integral equations generates a set of discretized integral equations, which can further be converted to a system of linear algebraic equations. This is accomplished by testing the discretized integral equations using the a set of test functions. In the method of moments, the Galerkin technique is typically used, which chooses the expansion basis functions as test functions. This leads to the following linear system:png]]-->
where <math>f_n^{(J)}</math> and <math>f_k^{(M)}</math> are the generalized vector basis functions for the expansion of electric and magnetic currents, respectively, and <math>I_n^{(J)}</math> and <math>V_k^{(M)}</math> are the unknown amplitudes of these basis functions, which have to be determined. Substituting these expansions into the integral equations generates a set of discretized integral equations, which can further be converted to a system of linear algebraic equations. This is accomplished by testing the discretized integral equations using the a set of test functions. In the method of moments, the Galerkin technique is typically used, which chooses the expansion basis functions as test functions. This leads to the following linear system: :<math>\begin{bmatrix}Z^{(EJ)} & T^{(EM)} \\U^{(HJ)} & Y^{(HM)}\end{bmatrix} \cdot \begin{bmatrix}I^{(J)} \\V^{(M)}\end{bmatrix} = \begin{bmatrix}V^{(E)} \\I^{(M)}\end{bmatrix} </math><!--[[File:PMOM3.png]]-->
where
:<math> Z_{ij}^{(EJ)} = \iiint\limits_{V_i} dv f_i^{(J)}(r) \cdot \iiint\limits_{V_j} dv' \overline{\overline{G}}_{EJ}(r|r') \cdot f_i^{(J)}(r')</math><!--[[File:PMOM6.png]]-->
and
:<math> V_i^{(E)} = \iiint\limits_{V_i} dv f_i^{(J)}(r) \cdot E^{inc}(r) </math>Â Â :<math> I_i^{(H)} = \iiint\limits_{V_i} dv f_i^{(M)}(r) \cdot H^{inc}(r) </math><!--[[File:PMOM7.png]]-->
Similar expressions can be derived for the T<sup>(EM)</sup>, U<sup>(HJ)</sup> and Y<sup>(HM)</sup>elements of the MoM matrix.