Fast summation of double infinite modal series using the Poisson summation formula

The main aim of this work is to verify the effectiveness of Poisson’s transformation in the summation of multiple-valued, double infinite modal series, encountered in the computational electromagnetism related to analysis of shielded microstrip circuits. In this contribution, the Poisson summation formula has been applied to accelerate the rate of convergence of the static part of the modal series under consideration in order to enable the effective application of Kummer’s transformation. The need for the use of Poisson’s formula has resulted from the fact that the studied modal series is a multiple-valued one and hence the conventional approach based on the complex contour integral method can not be exploited. Finally, the use of Kummer’s transformation in conjunction with Poisson’s summation formula has proved to be very efficient and enabled radical savings in computational time. This feature makes the proposed method a good candidate for practical applications, especially for electromagnetic CAD tools.