A comparison of numerical methods to obtain RCS using physical optics

For the solution of high frequency scattering by large complex objects the physical optics (PO) technique is well established. Of considerable interest is the accurate evaluation, using PO, of the RCS of curved patches, and to a lesser extent flat surfaces with curved boundaries. The application of PO to these geometries requires the solution of a double integral over the surface. In general the evaluation of this integral is not a simple task and approximate numerical techniques must be applied. In this paper a number of numerical techniques are investigated and their performance (computational speed and accuracy) is evaluated. The numerical techniques studied are: direct numerical integration, Gordon´s method (1975), the stationary phase method (Madurasinghe and Anderson 1994), and solution by FFT. The geometry considered for this study is an infinitely thin perfectly conducting net disc. This surface shape is chosen because the PO integration can be reduced to a single variable and it represents a test case in which the accuracy of each method can be calculated for a given radius of curvature. The findings of this study can he easily extended to the analysis of curved patches and to geometries of varying curvature.