| In this study, higher order modeling in both the geometry and the basis function is developed for the problem of electromagnetic scattering by arbitrarily shaped objects. The electric field integral equation and the magnetic field integral equation are formulated in the frequency domain using the vector and scalar potential descriptions. Objects are discretized using curvilinear triangles and comparisons are made with the results from objects discretized with the standard planar triangles. It is shown that curvilinear triangles provide quicker convergence of the moment method solution than do planar triangles, especially for quantities such as radar cross section and resonant frequency. As part of this analysis, techniques are developed and applied to the problem of integrating singular potentials over a curvilinear triangular surface. A formulation is presented for higher order bases and results are obtained for the first-order case. It is found that a solution using higher order bases usually requires fewer unknowns to obtain accurate results than in the zero-order case. Higher order bases generally perform poorly near edges; hence, basis functions which incorporate charge singularities are derived and tested. These basis functions provide a more accurate description of the current in the neighborhood of sharp edges than basis functions that do not account for charge singularities. |
