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We introduce and demonstrate a new error control scheme for the computation of far-zone interactions in the multilevel fast multipole algorithm when implemented within a multiple-precision arithmetic framework. The proposed scheme provides the optimum truncation numbers as well as the machine precisions given the desired relative error thresholds and the box sizes for the translation operator at all frequencies. In other words, unlike the previous error control schemes which are valid only for high-frequency problems, the proposed scheme can be used to control the error across both low-and high-frequency problems. Optimum truncation numbers and machine precisions are calculated for a wide range of box sizes and desired relative error thresholds with the proposed error control scheme. The results are compared with the previously available methods and numerical surveys.

Closed-form Green's function (CFGF) representations are developed for tangential magnetic current sources to calculate the mutual coupling between apertures on perfectly conducting circular cylinders covered with dielectric layers. The new representations are obtained by first rewriting the corresponding spectral domain Green's function representations in a different form (so that accurate results for electrically large cylinders, and along the axial line of a cylinder can be obtained). Then, the summation over the cylindrical eigenmodes is calculated efficiently. Finally, the resulting expressions are transformed to the spatial domain using a modified two-level generalized pencil of function method. Numerical results are presented showing good agreement when compared to CST Microwave Studio results.Index Terms-Aperture antennas, closed-form Green's functions, generalized pencil of function (GPOF) method, mutual coupling.

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