Sencer KOÇ, Mehmet ÇİYDEM

Wavefront-ray grid FDTD algorithm

A finite difference time domain algorithm on a wavefront-ray grid (WRG-FDTD) is proposed in this study to reduce numerical dispersion of conventional FDTD methods. A FDTD algorithm conforming to a wavefront-ray grid can be useful to take into account anisotropy effects of numerical grids since it features directional energy flow along the rays. An explicit and second-order accurate WRG-FDTD algorithm is provided in generalized curvilinear coordinates for an inhomogeneous isotropic medium. Numerical simulations for a vertical electrical dipole have been conducted to demonstrate the benefits of the proposed method. Results have been compared with those of the spherical FDTD algorithm and it is showed that numerical grid anisotropy can be reduced highly by WRG-FDTD.

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[1] Yee KS. Numerical solution of initial boundary value problems involving Maxwells equations in isotropic media. IEEE T Antenn Propag 1966; 14: 302-307.
[2] Taflove A, Hagness SC. Computational ElectrodynamicsThe Finite Difference Time Domain Method. 3rd ed. Boston, MA, USA: Artech House, 2005.
[3] Farjadpour A, Roundy D, Rodriguez A, Ibanescu M, Bermel P, Joannopoulos JD, Johnson SG, Burr GW. Improving accuracy by subpixel smoothing in the finite-difference time domain. Opt Lett 2006; 31: 2972-2974.
[4] Holland R. Finite difference solution of Maxwells equations in generalized non-orthogonal coordinates. IEEE T Nucl Sci 1983; 30: 4589-4591.
[5] Stratton JA. Electromagnetic Theory. New York, NY, USA; McGraw-Hill, 1941.
[6] Fusco M. FDTD algorithm in curvilinear coordinates. IEEE T Antenn Propag 1990; 38: 76-89.
[7] Fusco M, Smith MV, Gordon LW. Three-dimensional FDTD algorithm in curvilinear coordinates. IEEE T Antenn Propag 1991; 39: 1463-1471.
[8] Lee JF, Palandech R, Mittra R. Modeling three-dimensional discontinuities in waveguides using nonorthogonal FDTD algorithm. IEEE T Microw Theory 1992; 40: 346-352.
[9] Jurgens TG, Taflove A, Umashankar KR, Moore TG. Finite difference time domain modelling of curved surfaces. IEEE T Antenn Propag 1992; 40: 357-366.
[10] Hao Y, Railton CJ. Analyzing electromagnetic structures with curved boundaries on Cartesian FDTD meshes. IEEE T Microw Theory 1998; 46: 82-88.
[11] Gedney S, Lansing FS, Rascode DL. Full wave analysis of microwave monolithic circuit devices using a generalized Yee algorithm based on an unstructured grid. IEEE T Microw Theory 1996; 44: 1393-1400.
[12] Krumpholz M, Katehi LPB. MRTD: New time domain schemes based on multiresolution analysis. IEEE T Microw Theory 1997; 45: 385-393.
[13] Liu QH. The PSTD algorithm: a time domain method requiring only two cells per wavelength. Microw Opt Technol Lett 1997; 1: 158-165.
[14] Wang S, Teixeira FL. A three-dimensional angle-optimized finite difference time domain algorithm. IEEE T Microw Theory 2003; 51: 811-817.
[15] Zygridis TT, Tsiboukis TD. Development of higher order FDTD schemes with controlled dispersion error. IEEE T Antenn Propag 2005; 53: 2952-2960.
[16] Zhang XQ, Nie ZP, Xia MY, Qu SW, Li YH. Novel FDTD method with low numerical dispersion and anisotropy. In: PIERS Proceedings; 2023 March 2011; Marrakesh, Morocco. pp. 718-721.
[17] Kong Y, Chu Q, Li R. Two efficient unconditionally stable four stages split step FDTD methods with low numerical dispersion. PIER B 2013; 48: 1-22.
[18] Liu Y. Fourier analysis of numerical algorithms for the Maxwell equations. J Comput Phys 1996; 124: 396-416.
[19] Navarro EA, Wu C, Chung PY, Litva J. Some considerations about the finite difference time domain method in general curvilinear coordinates. IEEE Microw Guided W 1994; 4: 396-398.
[20] Ray SL. Numerical dispersion and stability characteristics of time-domain methods on nonorthogonal meshes. IEEE T Antenn Propag 1993; 41: 233-235.
[21] Nilavalan R, Craddock IJ, Railton CJ. Quantifying numerical dispersion in non-orthogonal FDTD meshes. IEE P-Microw Anten P 2002; 149: 23-27.
[22] Ciydem M, Koc S. FDTD algorithm on wavefront-ray grid for wave propagation. In: IEEE APS/URSI Symposium; July 2006; Albuquerque, NM, USA. pp. 3821-3824.
[23] Holland R. THREDS: A finite-difference time-domain EMP code in 3D spherical coordinates. IEEE T Nucl Sci 1983; 3: 4592-4595.