An Efficient Numerical Method for Determining Main Operating Frequency of Mandelbrot Fractal Patch Antennas

This paper proposes a numerical method to determine the main operating frequency of a Mandelbrot fractal patch antenna. The method involves a conformal transformation, mapping the antenna's complex boundaries in physical space to a simpler computational space represented by a cylinder. This transformation maintains constant electromagnetic boundary conditions, and the finite difference method ensures a transparency of the circular contour in the truncated finite element mesh. This method offers a significant saving on computational resource as validated through analytical, numerical, and experimental tests.