On the Numerical Dispersion of the Radial Point Interpolation Meshless (RPIM) Method in Lossy Media
Keywords:
Gaussian basis function, multiquadric basis function, numerical dispersion, radial point interpolation method (RPIM)Abstract
A general formula for numerical dispersion of the two-dimensional time-domain radial point interpolation meshless (2-D RPIM) method is analytically derived. Numerical loss and dispersion characteristics of the RPIM method with both Gaussian and multiquadric basis functions are investigated. It is found that numerical loss and dispersion errors of the RPIM vary with types of basis functions used and associated parameters, number of the nodes, and medium conductivities. In addition, condition numbers of the moment matrix of the meshless methods can also increase numerical dispersion errors. With a reasonable condition number of the moment matrix, the radial point interpolation meshless methods perform generally better than the FDTD method in terms of numerical dispersion errors.
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S. Yang, Z. Chen, Y. Yu, and S. Ponomarenko, “On the numerical dispersion of the radial point interpolation meshless method,” IEEE Microwave And Wireless Components Letters, vol. 24, no. 10, pp. 653-655, Oct. 2014.
T. Kaufmann, C. Fumeaux, and R. Vahldieck, “The meshless radial point interpolation method for time-domain electromagnetics,” 2008 IEEE MTTS International Microwave Symposium Digest, Atlanta, USA, pp. 61-64, Sep. 2008.
Y. Yu, F. Jolani, and Z. Chen, “An efficient meshless approach to multi-scale modeling in the time-domain,” The Applied Computational Electromagnetics Society, vol. 27, no. 6, pp. 466-474, June 2012.
Y. Yu and Z. Chen, “A 3-D radial point interpolation method for meshless time-domain modeling,” IEEE Transactions on Microwave Theory and Techniques, vol. 57, no. 8, pp. 2015-2020, Aug. 2009.
R. M. S. de Oliveira, W. C. B. Sousa, and W. R. M. Rabelo, “A meshless discretization methodology based on lennard-jones forces,” IEEE Antennas and Wireless Propagation Letters, vol. 16, pp. 1492-1495, June 2017.
Y. Tanaka, S. Watanabe, and T. Oko, “Study of eddy current analysis by a meshless method using RPIM,” IEEE Transactions on Magnetics, vol. 51, no. 3, pp. 7201404, Mar. 2015.
R. Khalef, M. T. Benhabiles, F. Grine, and M. L. Riabi, “An unconditionally stable radial point interpolation meshless method based on the Crank– Nicolson scheme solution of wave equation,” IEEE Transactions on Microwave Theory and Techniques, vol. 66, no. 8, pp. 3705-3713, Aug. 2018.
T. Kaufmann, C. Engström, C. Fumeaux, and R. Vahldieck, “Eigenvalue analysis and longtime stability of resonant structures for the meshless radial point interpolation method in time domain,” IEEE Transactions on Microwave Theory and Techniques, vol. 58, no. 12, pp. 3399-3408, Dec. 2010.
Y. Zhang, K. R. Shao, Y. Guo, J. Zhu, D. X. Xie, and J. D. Lavers, “A comparison of point interpolative boundary meshless method based on PBF and RBF for transient eddy-current analysis,” IEEE Transactions on Magnetics, vol. 43, no. 4, pp. 1497-1500, Apr. 2007.
S. J. Lai, B. Z. Wang, and Y. Duan, “Meshless radial basis function method for transient electromagnetic computations,” IEEE Trans. Magnetics, vol. 44, no. 10, pp. 2288-2295, Oct. 2008.
F. Ansarizadeh and M. Movahhedi, “Unconditionally-stable meshless methods using different splitstep techniques and their phase velocity considerations,” The Applied Computational Electromagnetics Society, vol. 28, no. 9, pp. 788-794, Sep. 2013.
X. Zhang, P. Ye, Z. Chen, and Y. Yu, “Numerical dispersion analysis of radial point interpolation meshless method,” 2017 Progress in Electromagnetics Research Symposium, Singapore, pp. 717- 719, Nov. 2015.
Z. Shaterian, T. Kaufmann, and C. Fumeaux, “On the choice of basis functions for the meshless radial point interpolation method with small local support domains,” IEEE International Conference on Computational Electromagnetics, Hong Kong, China, pp. 288-290, Feb. 2015.
Z. Chen and S. Luo, “Generalization of the finitedifference-based time-domain methods using the method of moments,” IEEE Transactions on Microwave Theory and Techniques, vol. 54, no. 9, pp. 2515-2524, Sep. 2006.
G. Sun and C. W. Trueman, “Numerical dispersion and numerical loss in explicit finite-difference time-domain methods in lossy media,” IEEE Transactions on Antennas and Propagation, vol. 53, no. 11, pp. 3684-3690, Nov. 2005.
J. A. Pereda, O. García, A. Vegas, and A. Prieto, “Numerical dispersion and stability analysis of the FDTD technique in lossy dielectrics,” IEEE Microwave and Guided Wave Letters, vol. 8, no. 7, pp. 245-247, July 1998.
G. Sun, X. Ma, and Z. Bai, “Numerical stability and dispersion analysis of the precise-integration time-domain method in lossy media,” IEEE Transactions on Microwave Theory and Techniques, vol. 60, no. 9, pp. 2723-2729, Sep. 2012.
Z. Chen and M. Ney, “Method of weighted residuals: a general approach to deriving timeand frequency-domain numerical methods,” IEEE Antennas and Propagation Magazines, vol. 51, no. 1, pp. 51-70, Feb. 2009.
Z. Chen, “How can we unify numerical methods with a single mathematic framework?,” Proceedings of 2014 Asia-Pacific Conference on Antennas and Propagation, Harbin, China, pp. 1392-1395, July 2014.
J. Wang, Z. Chen, J. Li, Y. Yu, and J. Liang, “Towards a unifying computational platform with the node-based meshless method,” Proceedings of 2018 IEEE International Microwave Symposium, Pennsylvania, USA, pp. 1017-1020, June 2018.
