We present a new approach based on numerical constructions of testing functions for improving the accuracy of the magnetic-field integral equation (MFIE) and the combined-field integral equation (CFIE) with low-order discretizations. Considering numerical solutions, testing functions are designed by enforcing the compatibility of the MFIE systems with the accurate coefficients obtained by solving the electric-field integral equation (EFIE). We demonstrate the accuracy improvements on scattering problems, where the testing functions are designed at a single frequency and used in frequency ranges to benefit from the design procedure. The proposed approach is easy to implement by using existing codes, while it improves the accuracy of MFIE and CFIE without deteriorating the efficiency of iterative solutions.
2. Ergül, Ö and L. Gürel, "Improving the accuracy of the MFIE with the choice of basis functions," Proc. IEEE Antennas and Propagation Soc. Int. Symp., Vol. 3, 3389-3392, 2004.
3. Ubeda, E. and J. M. Rius, "MFIE MOM-formulation with curl-conforming basis functions and accurate kernel integration in the analysis of perfectly conducting sharp-edged objects," Microw. Opt. Technol. Lett., Vol. 44, No. 4, 354-358, Feb. 2005.
4. Ergül, Ö and L. Gürel, "Improving the accuracy of the magnetic field integral equation with the linear-linear basis functions," Radio Sci., Vol. 41, RS4004, Jul. 2006.
5. Ubeda, E. and J. M. Rius, "Novel monopolar MFIE MoM-discretization for the scattering analysis of small objects," IEEE Trans. Antennas Propag., Vol. 54, No. 1, 50-57, Jan. 2006.
6. Ergül, Ö and L. Gürel, "Linear-linear basis functions for MLFMA solutions of magnetic-field and combined-field integral equations," IEEE Trans. Antennas Propag., Vol. 55, No. 4, 1103-1110, Apr. 2007.
7. Andriulli, F. P., K. Cools, H. Bagcı, F. Olyslager, A. Buffa, S. Christiansen, and E. Michielssen, "A multiplicative Calderon preconditioner for the electric field integral equation," IEEE Trans. Antennas Propag., Vol. 56, No. 8, 2398-2412, Aug. 2008.
8. Rao, S. M., D. R. Wilton, and A. W. Glisson, "Electromagnetic scattering by surfaces of arbitrary shape," IEEE Trans. Antennas Propag., Vol. 30, No. 3, 409-418, May 1982.
9. Ofluoğlu, A. E., T. Çiftçi, and Ö. Ergül, "Magnetic-field integral equation," IEEE Antennas Propag. Mag., Vol. 57, No. 4, 134-142, Aug. 2015.