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The combined field integral equation (CFIE) method is used to calculate the RF magnetic B1 field produced by a transmission-line resonator element for high-field magnetic resonance systems. The method calculates the surface currents on a homogeneous phantom with triangular patches with the Rao-Wilton-Glisson (RWG) basis functions, and the tetrahedra with the Schaubert-Wilton-Glisson (SWG) basis functions are used to calculate the resonator element field. The transmission-line resonator element is excited at its resonant frequency and the equivalent surface current distribution over the phantom are obtained, and then the internal fields in the phantom are calculated for the 9.4-T MRI system. This integral equation method provides much faster B1 field results than the corresponding finite-difference time domain (FDTD) approach. A field localization method by adjusting phase excitations is also discussed.