An Efficient Meshless Approach to Multi-scale Modeling in the Time-domain
Keywords:
Alternating-direction implicit scheme, finite-difference time-domain, hybrid methods, meshless methods, radial point interpolation methodAbstract
An efficient multi-scale approach to meshless modeling of three-dimensional guided wave problems is realized by hybridization of the radial point interpolation method (RPIM) and the unconditionally stable leapfrog alternatingdirection implicit (ADI-) RPIM scheme. In it, the solution domain is regionalized; the leapfrog ADIRPIM is applied to regions with coarse nodal distributions while the original RPIM is applied to the rest of the dense nodal solution domain. With application of the leapfrog ADI scheme, a uniform time-step can now be applied to the entire solution domain without temporal and spatial interpolation between different computational regions. Furthermore, in the proposed scheme, implicit updating of field variables is confined only within the regions of densely-distributed nodes, yielding a significant saving in memory overhead and a further reduction in CPU time in comparison with leapfrog ADI-RPIM and original RPIM, respectively.
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References
R. K. Gordon and W. E. Hutchcraft, “The Use of Multiquadric Radial Basis Functions in Open Region Problems,” Applied Computational Electromagnetics Society (ACES) Journal, vol. 21, no. 2, pp. 127 – 134, July 2006.
A. B. Ali, E. A. Hajlaoui, and A. Gharsallah, “Efficient Analysis Technique for Modeling Periodic Structures Based on Finite Element Method using High-Order Multiscalets Functions,” Applied Computational Electromagnetics Society (ACES) Journal, vol. 25, no. 9, pp. 755 - 763, September 2010.
J. G. Wang and G. R. Liu, “A Point Interpolation Meshless Method Based on Radial Basis Functions,” Int. J. Numer. Methods Eng., 2001.
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, 2008.
T. Kaufmann, C. Fumeaux, and R. Vahldieck, “The Meshless Radial Point Interpolation Method for Time-Domain Electromagnetic,” IEEE MTT-S Int. Microwave Symp. Dig., Atlanta GA, pp. 61-64, June 15-20, 2008.
S. J. Lai, B. Z. Wang, and Y. Duan, “Solving Helmholtz Equation by Meshless Radial Basis Functions Method,” Progress In Electromagnetics Research B, vol. 24, pp. 351-367, 2010.
Y. Yu and Z. Chen, “A Three-Dimensional Radial Point Interpolation Method for Meshless TimeDomain Modeling,” IEEE Trans. Microwave Theory & Techniques, vol. 57, no. 8, pp. 2015- 2020, 2009.
Y. Yu and Z. Chen, “Meshless RPIM Modeling of Open-Structures using PMLs,” IEEE MTT-S Int. Microwave Symp. Dig., Anaheim, May 23-28, 2010.
Y. Yu and Z. Chen, “Implementation of Material Interface Conditions in the Radial Point Interpolation Meshless Method,” IEEE Trans. Antennas and Propagation, vol. 59, no. 8, pp. 2916-2923, 2011.
Y. Yu and Z. Chen, “Towards the Development of Unconditionally Stable Time-Domain Meshless Numerical Methods,” IEEE Trans. Microwave Theory and Techniques, vol. 58, no. 3, pp. 578- 586, 2010.
T. Kaufmann, Y. Yu, C. Engström, Z. Chen, and C. Fumeaux “Recent Developments of the Meshless Radial Point Interpolation Method for TimeDomain Electromagnetics,” International Journal of Numerical Modelling: Electronic Networks, Devices and Fields, Article first published online :, DOI: 10.1002/jnm.1830, Feb. 15, 2012.
S. J. Cooke, M. Botton, T. M. Antonsen, and B. Levush, “A Leapfrog Formulation of the 3D ADIFDTD Algorithm,” Intl. Workshop on Computational Electromagnetics in Time-Domain, , pp. 1-4, Oct. 15-17, 2007
F. Zhen, Z. Chen, and J. Zhang, “Toward the Development of a Three-Dimensional Unconditionally Stable Finite Difference TimeDomain Method,” IEEE Trans. Microwave Theory & Techniques, vol. 48, no. 9, pp. 1550-1558, Sept. 2000.
T. Namiki, “3-D ADI-FDTD Method-- Unconditionally Stable Time-Domain Algorithm for Solving Full Vector Maxwell's Equations," IEEE Trans. Microwave Theory & Techniques, vol. 48, no. 10, pp. 1743-1748, Oct. 2000.
J. Chen and J. Wang, “An Unconditionally Stable Subcell Model for Thin Wires in the ADI-FDTD Method,” Applied Computational Electromagnetics Society (ACES) Journal, vol. 25, no. 8, pp. 659 - 664, August 2010.
J. A. Roden and S. D. Gedney, “Convolutional PML (CPML): An Efficient FDTD Implementation of the CFS-PML for Arbitrary Media,” Microwave Opt. Technol. Lett., vol. 27, pp. 334-339, Dec. 5, 2000.
S. D. Gedney, G. Liu, J. Alan Rodden, and A. Zhu, “Perfectly Matched Layer Media with CFS for an Unconditionally Stable ADI-FDTD Method," IEEE Trans. Antennas & Propagation, vol. 49, no. 11, pp. 1554-1559, 2001.
F. Xu and K. Wu, “Guided-Wave and Leakage Characteristics of Substrate Integrated Waveguide,” IEEE Trans. Microwave theory & techniques, vol. 53, no. 3, pp. 66-73, 2005.
