When employing computational methods for solving problems in electromagnetic scattering the resulting solutions are strongly determined by the geometry of the scatterer. Careful consideration must therefore be given to the computational geometry used in representing the scatterer. Here we show that the solution for a problem as simple as plane wave scattering off a PEC sphere is sensitive to the computational geometry used to represent the sphere. We show this by implementing 4 higher-order computational geometry schemes over 3 different tessellations resulting in 45 different representations of the sphere. Two methods for solving the scattering problem are implemented: the boundary-element method (BEM) based on the MFIE, and the physical optics (PO) method. Results are compared and insights are obtained into the performance of the various schemes to model surfaces accurately and efficiently. The comparison of the different schemes takes into consideration the required computational resources in implementing the schemes. Some unexpected results are discovered and explanations given.
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