Stability of the high frequency fast multipole method for Helmholtz' equation in three dimensions

BIT Numerical Mathematics

Volumn 44, Issue 4, 2004, Pages 773-791

  Nilsson, Martin ^a  

^a UPPSALA UNIVERSITY   (Sweden)

Author keywords

Error estimate; Fast Multipole Method; Helmholtz' equation; Stability

Indexed keywords

EID: 18244390721     PISSN: 00063835     EISSN: None     Source Type: Journal    
DOI: 10.1007/s10543-004-4412-8     Document Type: Article

References (12)

1. G. B. Arfken and H. J. Weber, Mathematical Methods for Physicists, 4th ed., Academic Press, San Diego, 1995.
2. W. C. Chew, J. Jin, E. Michielssen and J. Song, Fast and Efficient Algorithms in Computational Electromagnetics, Artech House, Norwood, 2001.
3. R. Coifman, V. Rokhlin and S. Wandzura, The fast multipole method for the wave equation: A pedestrian prescription, IEEE Trans. Antennas and Propagation, 35 (1993), pp. 7-12.
4. E. Darve, The fast multipole method I: Error analysis and asymptotic complexity, SIAM J. Numer. Anal., 38 (2000), pp. 98-128.
5. E. Darve, The fast multipole method: Numerical implementation, 3. Comput. Phys., 160 (2000), pp. 195-240.
6. G. H. Golub and C. F. Van Loan, Matrix Computations, 3rd ed., The Johns Hopkins Press, Baltimore, MD, 1996.
7. L. Greengard, J. Huang, V. Rokhlin and S. Wandzura, Accelerating fast multipole methods for the Helmholtz equation at low frequencies, IEEE Comput. Sci. and Eng., 5 (1998), pp. 32-38.
8. M. L. Hastriter, S. Ohnuki and W. C. Chew, Error control of the translation operator in 3D MLFMA, Microwave Opt. Tech. Lett., 37 (2003), pp. 184-188.
9. M. Nilsson, A parallel shared memory implementation of the fast multipole method for electromagnetics, Tech. Report 2003-049, Dept. Info. Tech., Sci. Comp., Uppsala University, Sweden, 2003.
10. S. Ohnuki and W. C. Chew, Numerical accuracy of multipole expansion for 2D MLFMA, IEEE Trans. Antennas and Propagation, 51 (2003), pp. 1883-1890.
11. V. Rokhlin, Diagonal forms of translation operators for the Helmholtz equation in three dimensions, Appl. Comput. Harmon. Anal., 1 (1993), pp. 82-93.
12. J. Song and W. C. Chew, Multilevel fast multipole algorithm for solving combined field integral equation of electromagnetic scattering, Microwave Opt. Tech. Lett., 10 (1995), pp. 14-19.