The quadrilateral patch modeling using a generalized roof-top vector basis function

Two typical modeling techniques of the method of moments are wire-grid modeling and surface patch modeling. We model an arbitrary scattering object by quadrilateral patches. The unknown current on the structure is then expanded by generalized roof-top vector basis functions and the Galerkin´s method is applied. To evaluate elements of the impedance matrix, we derive some equations necessary for the numerical calculation. When the source and observation points coincide, the integrand becomes singular so that one needs to treat them separately. To overcome this difficulty, the singular function inside the surface integral is approximated by a linear function. Then the integrand is evaluated by using a non-linear transformation. It is shown that the final expression using the above procedure can be represented in summation form with several analytic functions. Brief theoretical analysis and numerical examples are given. The final results of the approach are compared with those using the triangular patches with roof-top basis functions.