Search
Acceleration of the Discrete Green’s Function Formulation of the FDTD Method Based on Recurrence Schemes
Abstract
In this paper, we investigate an acceleration of the discrete Green's function (DGF) formulation of the FDTD method (DGF-FDTD) with the use of recurrence schemes. The DGF-FDTD method allows one to compute FDTD solutions as a convolution of the excitation with the DGF kernel. Hence, it does not require to execute a leapfrog time-stepping scheme in a whole computational domain for this purpose. Until recently, the DGF generation has been the limiting step of DGF-FDTD due to large computational resources, in terms of processor time and memory, required for these computations. Hence, we have derived the no-neighbours recurrence scheme for one-dimensional FDTD-compatible DGF using solely properties of the Gauss hypergeometric function (GHF). Using known properties of GHF, the recurrence scheme is obtained for arbitrary stable time-step size. In this paper, we show that using the recurrence scheme, computations of 1-D FDTD solutions with the use of the DGF-FDTD method can be around an order of magnitude faster than those based on the direct FDTD method. Although 2- and 3-D recurrence schemes for DGF (valid not only for the magic time-step size) still need to be derived, the 1-D case remains the starting point for any research in this area.
Authors (2)
-
Jacek Gulgowski
Cite as
Full text
- Publication version
- Accepted or Published Version
- License
- Copyright (2019, IEEE)
Keywords
Details
- Category:
- Conference activity
- Type:
- publikacja w wydawnictwie zbiorowym recenzowanym (także w materiałach konferencyjnych)
- Language:
- English
- Publication year:
- 2019
- Bibliographic description:
- Gulgowski J., Stefański T.: Acceleration of the Discrete Green’s Function Formulation of the FDTD Method Based on Recurrence Schemes// / : , 2019,
- Bibliography: test
-
show (20) hide
- A. Taflove and S. C. Hagness, Computational Electrodynamics: The Finite-difference Time-domain Method , 3rd edition, Artech House, Boston, 2005. open in new tab
- J. Vazquez, C. G. Parini, "Discrete Green's function formulation of FDTD method for electromagnetic modelling," Electron. Lett., vol. 35, no. 7, pp. 554-555, 1999. open in new tab
- W. Ma, M. R. Rayner, C. G. Parini, "Discrete Green's function formu- lation of the FDTD method and its application in antenna modeling," IEEE Trans. Antennas Propag., vol. 53, no. 1, pp. 339-346, 2005. open in new tab
- R. Holtzman, R. Kastner, E. Heyman, and R. W. Ziolkowski, "Stability analysis of the Green's function method (GFM) used as an ABC for arbitrarily shaped boundaries," IEEE Trans. Antennas Propag., vol. 50, no. 7, pp. 1017-1029, 2002. open in new tab
- R. Kastner, "A multidimensional Z-transform evaluation of the discrete finite difference time domain Green's function," IEEE Trans. Antennas Propag., vol. 54, no. 4, pp. 1215-1222, 2006. open in new tab
- N. Rospsha, R. Kastner, "Closed form FDTD-compatible Green's func- tion based on combinatorics," J. Computat. Phys., vol. 226, no. 1, pp. 798-817, 2007. open in new tab
- S.-K. Jeng, "An analytical expression for 3-D dyadic FDTD-compatible Green's function in infinite free space via Z-transform and partial difference operators," IEEE Trans. Antennas Propag., vol. 59, no. 4, pp. 1347-1355, 2011. open in new tab
- T. P. Stefański, "A new expression for the 3-D dyadic FDTD-compatible Green's function based on multidimensional Z-transform," IEEE Anten- nas Wirel. Propag. Lett., vol. 14, pp. 1002-1005, 2015. open in new tab
- T. P. Stefański, "Discrete Green's function approach to disjoint domain simulations in 3D FDTD method," Electron. Lett., vol. 49, no. 9, pp. 597-598, 2013. open in new tab
- T. P. Stefański, "Hybrid technique combining the FDTD method and its convolution formulation based on the discrete Green's function," IEEE Antennas Wirel. Propag. Lett., vol. 12, pp. 1448-1451, 2013. open in new tab
- T. P. Stefański, "Electromagnetic problems requiring high-precision computations," IEEE Antennas Propag. Mag., vol. 55, no. 2, pp. 344- 353, 2013. open in new tab
- B. P. de Hon, J. M. Arnold, "Recursive evaluation of space-time lattice Green's functions," J. Phys. A: Math. Theor., vol. 45, 385202, 2012. open in new tab
- B. P. de Hon, S. J. Floris, J. M. Arnold, "No-neighbours recurrence schemes for space-time Green's functions on a 3D simple cubic lattice," J. Phys. A: Math. Theor., vol. 51, 085201, 2018. open in new tab
- M. S. Min, C. H. Teng, "The instability of the Yee scheme for the "magic time step"," J. Computat. Phys., vol. 166, no. 2, pp. 418-424, 2001. open in new tab
- R. F. Remis, "On the stability of the finite-difference time-domain method," J. Computat. Phys., vol. 163, no. 1, pp. 249-261, 2000. open in new tab
- J. Gulgowski, T. P. Stefański, "Recurrence scheme for FDTD-compatible discrete Green's function derived based on properties of Gauss hyperge- ometric function," Journal of Electromagnetic Waves and Applications, pp. 1-17, DOI 10.1080/09205071.2019.1568308, 2019. open in new tab
- W. Koepf, Hypergeometric Summation , Springer-Verlag, London, 2014. open in new tab
- H. Bateman, Higher Transcendental Functions Vol. I-III., McGraw-Hill Book Company, New York, 1953.
- R. Vidunas, "Contiguous relations of hypergeometric series," J. Comp. Appl. Math. , vol. 153, pp. 507-519, 2003. open in new tab
- A. K. Ibrahim, M. A. Rakha, "Contiguous relations and their compu- tations for 2 F 1 hypergeometric series," Comput. Math. Appl. , vol. 56, pp. 1918-1926, 2008.
- Verified by:
- Gdańsk University of Technology
seen 75 times