Zhurnal Radioelektroniki - Journal of Radio Electronics. ISSN 1684-1719. 2020. No. 4
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Full text in Russian (pdf)
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DOI 10.30898/1684-1719.2020.4.7
 

Using Gauss-Legendre and Hermit quadrature formulas for calculating integrals in fast-multipole algorithm

 

Е.I. Lavretski

AO NII of Precise Constructions, Dekabristov str., 51, Moscow 127490, Russia

 

The paper is received on March 31, 2020

 

Abstract: The effective method was developed for calculation of solid angle integrals arising in solving electric field integral equations with the help of fast multipole algorithm (FMA) or multi-level fast multipole algorithm (MLFMA). It has been suggested to replace variables in integrated functions to obtain algebraic polynomials from trigonometric polynomials and, thus, calculate the integrals with the help of Gauss-Legendre and Hermit quadrature formulas. The method permits exact calculations of mutual impedances with minimal quadratures and substantial reduction of required memory for saved arrays and the resulting improvement of performance in fast multipole algorithms.

Key words: FMA and MLFMA, solid angle integration, Gaussian and Hermit quadrature formulas.

References

1. Coifman R., Rokhlin V., Vandzura S. The fast multipole method for the wave equation: a pedestrian prescription. IEEE Antennas and Propagation Magazine. 1993. Vol.35. No.3. P.7-12.

2. Darve E. The fast multipole method: numerical implementation. Int. J. of Computational Physics. 2000., Vol.160. No.1. P.195-240.

3. Chew W., Jin J., Michielssen E. and Song J. Fast and efficient algorithms in computational electromagnetics. 2001. House. 2002. 931 p.

4. Gibson W. The method of moments in electromagnetics. Chapman & Hall. 2008.

5. Volakis J., Sertel K. Integral equation methods for electromagnetics. Scitech Publishing. 2012. 391 p.

6. Ergül O., Gürel L. The multilevel fast multipole algorithm (MLFMA) for solving large-scale computational electromagnetics problems. IEEE Press. 2014. 493 p.

7. Markov G.T., Chaplin A.F. Vozbuzhdeniye elektromagnitnykh voln [Excitation of electromagnetic waves]. Moscow, Energiya Publ. 1967. 371 p. (in Russian)

8. Stratton J. Electromagnetic Theory. McGraw-Hill, 1941. 539 p.

9. Abramowitz M., Stegun I. Handbook of mathematical functions. National Bureau of Standards. 1970. 1045 p.

10. Rao S., Wilton D., Glisson A. Electromagnetic scattering by surfaces of arbitrary shape. IEEE Trans. on Antennas and Propagation. 1982. Vol.30. No.3. P.409-418.

11. Maaskant R. Analysis of large antenna systems. PhD Thesis. Eindhoven Technische University. 2010. 273 p.

 

For citation:

Lavretski E.I. Using Gauss-Legendre and Hermit quadrature formulas for calculating integrals in fast-multipole algorithm. Zhurnal Radioelektroniki - Journal of Radio Electronics. 2020. No. 4. Available at http://jre.cplire.ru/jre/apr20/7/text.pdf.  DOI 10.30898/1684-1719.2020.4.7