This work presents a fast computational algorithm that can be used as an alternative to the conventional surface-integral evaluation method included in the electric field integral equation (EFIE) technique when applied to a triangular-patch model for conducting surfaces of arbitrary-shape. Instead of evaluating the integrals by transformation to normalized area coordinates, they are evaluated directly in the Cartesien coordinates by dividing each triangular patch to a finite number of small triangles. In this way, a large number of double integrals is replaced by a smaller number of finite summations, which considerably reduces the time required to get the current distribution on the conducting surface without affecting the accuracy of the results. The proposed method is applied to flat and curved surfaces of different categories including open surfaces possessing edges, closed surfaces enclosing cavities and cavity-backed apertures. The accuracy of the proposed computations is realized in all of the above cases when the obtained results are compared with those obtained using the area coordinates method as well as when compared with some published results.
2. Hertel, T. W. and G. S. Smith, "On the dispersive properties of the conical spiral antenna and its use for pulsed radiation," IEEE Trans. Antennas. Propagat., Vol. 51, No. 7, 1426-1433, 2003.
3. Rao, S. M. and D. R. Wilton, "Transient scattering by conducting surfaces of arbitrary shape," IEEE Trans. Antennas Propagat., Vol. 39, No. 1, 56-61, 1991.
4. Sarkar, T. K., W. Lee, and S. M. Rao, "Analysis of transient scattering from composite arbitrarily shaped complex structures," IEEE Trans. Antennas Propagat., Vol. 48, No. 10, 1625-1634, 2000.
5. Rao, S. M., D. R. Wilton, and A. W. Glisson, "Electromagnetic scattering by surfaces of arbitrary shape," IEEE Trans. Antennas Propagat., Vol. 30, No. 5, 409-418, 1982.
6. Yla-Oijala, P., M. Taskinen, and J. Sarvas, "Surface integral equation method for general composite metallic and dielectric structures with junctions," Progress In Electromagnetic Research, Vol. 52, 81-108, 2005.
7. Shore, R. A. and A. D. Yaghjian, "A low-order-singularity electric- field integral equation solvable with pulse basis functions and point matching," Progress In Electromagnetic Research, Vol. 52, 129-151, 2005.
8. Zienkiewicz, O. C., The Finite Element Method in Engineering Science, McGraw-Hill, New York, 1971.
9. Taylor, D. J., "Accurate and efficient numerical integration of weakly singular integrals in Galerkin EFIE Solutions," IEEE Trans. Antennas Propagat., Vol. 51, No. 7, 1630-1637, 2003.
10. Bluck, M. J., M. D. Pocock, and S. P. Walker, "An accurate method for the calculation of singular integrals arising in time- domain integral equation analysis of electromagnetic scattering," IEEE Trans. Antennas Propagat., Vol. 45, No. 12, 1793-1798, 1997.
11. Wilton, D. R., S. M. Rao, A. W. Glisson, D. H. Schaubert, O. M. Al-Bundak, and C. M. Butler, "Potential integrals for uniform and linear source distributions on polygonal domains," IEEE Trans. Antennas Propagat., Vol. 32, No. 3, 276-281, 1984.
12. Hanninen, I., M. Taskinen, and J. Sarvas, "Singularity subtraction integral formulation for surface integral equations with RWG rooftop and hybrid basis functions," Progress In Electromagnetic Research, Vol. 63, 243-278, 2006.