Fast summation of double infinite modal series using the Poisson summation formula
Institute of Telecommunications and Acoustics, Wrocław University of Technology
Wyb. Wyspiańskiego 27, 50-370 Wrocław, Poland
e-mail: Piotr.Slobodzian@pwr.wroc.pl
Received:
Rec. 17 June 2004
DOI: 10.12921/cmst.2005.11.01.57-61
OAI: oai:lib.psnc.pl:582
Abstract:
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.
Key words:
convergence acceleration, IE-MoM approach, Poisson’s summation formula, series transformation
References:
[1] P. M. Słobodzian, Fast summation of double infinite modal series involved in analysis of shielded microstrip circuits, CMST 10, 5-15 (2003).
[2] R. Lampe, P. Klock and P. Mayes, Integral Transforms Useful for the Accelerated Summation of Periodic, Free- Space Green’s Functions, IEEE Trans. Microwave Theory and Tech., 33, 734-736 (1985).
[3] P. M. Morse and H. Feshbach, Methods of theoretical physics, McGraw-Hill Book Co., Inc., New York, 1953.
[4] M. Abramowitz and I. A. Stegun, Handbook of mathematical functions, Dover Pub., Inc., New York, 1970.
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.
Key words:
convergence acceleration, IE-MoM approach, Poisson’s summation formula, series transformation
References:
[1] P. M. Słobodzian, Fast summation of double infinite modal series involved in analysis of shielded microstrip circuits, CMST 10, 5-15 (2003).
[2] R. Lampe, P. Klock and P. Mayes, Integral Transforms Useful for the Accelerated Summation of Periodic, Free- Space Green’s Functions, IEEE Trans. Microwave Theory and Tech., 33, 734-736 (1985).
[3] P. M. Morse and H. Feshbach, Methods of theoretical physics, McGraw-Hill Book Co., Inc., New York, 1953.
[4] M. Abramowitz and I. A. Stegun, Handbook of mathematical functions, Dover Pub., Inc., New York, 1970.
