A nonuniform cylindrical FDTD algorithm with improved PML and quasi-PML absorbing boundary conditions

Many applications require time-domain solutions of Maxwell's equations in inhomogeneous, conductive media involving cylindrical geometries with both electrically small and large structures. The conventional finite-difference time-domain (FDTD) method with a uniform Cartesian grid will result in a staircasing error, and wastes many unnecessary cells in regions with large structures in order to accommodate the accurate geometrical representation in regions with small structures. In this work, an explicit FDTD method with a nonuniform cylindrical grid is developed for time-domain Maxwell's equations. A refined lattice is used near sharp edges and within fine geometrical details, while a larger lattice is used outside these regions. This provides an efficient use of limited computer memory and computation time. The authors use two absorbing boundary conditions to a nonuniform cylindrical grid: (1) the straightforward extension of Berenger's perfectly matched layer (PML) which is no longer perfectly matched for cylindrical interfaces, thus the name quasi-PML, (QPML); (2) the improved true PML based on complex coordinates. In practice, both PML schemes can provide a satisfactory absorbing boundary condition. Numerical results are shown to compare the two absorbing boundary conditions (ABCs) and to demonstrate the effectiveness of the nonuniform grid and the absorbing boundary conditions.

[1]  Q. Liu,et al.  Quasi‐PML for waves in cylindrical coordinates , 1998 .

[2]  Weng Cho Chew,et al.  Analytical derivation of a conformal perfectly matched absorber for electromagnetic waves , 1998 .

[3]  W. Chew,et al.  Systematic derivation of anisotropic PML absorbing media in cylindrical and spherical coordinates , 1997 .

[4]  Weng Cho Chew,et al.  PML-FDTD in cylindrical and spherical grids , 1997 .

[5]  Jian-Ming Jin,et al.  Complex coordinate stretching as a generalized absorbing boundary condition , 1997 .

[6]  E. Michielssen,et al.  Complex coordinate system as a generalized absorbing boundary condition , 1997, IEEE Antennas and Propagation Society International Symposium 1997. Digest.

[7]  Jan S. Hesthaven,et al.  Spectral Simulations of Electromagnetic Wave Scattering , 1997 .

[8]  Stephen D. Gedney,et al.  EFFICIENT IMPLEMENTATION OF THE UNIAXIAL-BASED PML MEDIA IN THREE-DIMENSIONAL NONORTHOGONAL COORDINATES WITH THE USE OF THE FDTD TECHNIQUE , 1997 .

[9]  Qing Huo Liu,et al.  AN FDTD ALGORITHM WITH PERFECTLY MATCHED LAYERS FOR CONDUCTIVE MEDIA , 1997 .

[10]  Qing Huo Liu,et al.  PERFECTLY MATCHED LAYERS FOR ELASTODYNAMICS: A NEW ABSORBING BOUNDARY CONDITION , 1996 .

[11]  J. Bérenger.  Three-Dimensional Perfectly Matched Layer for the Absorption of Electromagnetic Waves , 1996 .

[12]  W. Chew,et al.  Elongated 3D FDTD modeling using PML , 1996, IEEE Antennas and Propagation Society International Symposium. 1996 Digest.

[13]  Q.H. Liu,et al.  Using perfectly matched layers for elastodynamics , 1996, IEEE Antennas and Propagation Society International Symposium. 1996 Digest.

[14]  Jiayuan Fang,et al.  Generalized perfectly matched layer-an extension of Berenger's perfectly matched layer boundary condition , 1995 .

[15]  Omar M. Ramahi,et al.  Complementary operators: a method to annihilate artificial reflections arising from the truncation of the computational domain in the solution of partial differential equations , 1995 .

[16]  Allen Taflove,et al.  Computational Electrodynamics the Finite-Difference Time-Domain Method , 1995 .

[17]  Chen Wu,et al.  Modeling of waveguide structures using the nonorthogonal FDTD method with a PML absorbing boundary , 1995 .

[18]  Jean-Pierre Berenger,et al.  A perfectly matched layer for the absorption of electromagnetic waves , 1994 .

[19]  Chen Wu,et al.  Application of PML superabsorbing boundary condition to non-orthogonal FDTD method , 1994 .

[20]  Weng Cho Chew,et al.  A 3D perfectly matched medium from modified maxwell's equations with stretched coordinates , 1994 .

[21]  Endre Süli,et al.  Error estimates for Yee's method on non-uniform grids , 1994 .

[22]  E. Süli,et al.  A convergence analysis of Yee's scheme on nonuniform grids , 1994 .

[23]  R. Luebbers,et al.  The Finite Difference Time Domain Method for Electromagnetics , 1993 .

[24]  Qing Huo Liu,et al.  Electromagnetic field generated by an off-axis source in a cylindrically layered medium with an arbitrary number of horizontal discontinuities , 1993 .

[25]  Qing Huo Liu,et al.  Diffraction of nonaxisymmetric waves in cylindrically layered media by horizontal discontinuities , 1992 .

[26]  W. Chew.  Waves and Fields in Inhomogeneous Media , 1990 .

[27]  A. Bayliss,et al.  Radiation boundary conditions for wave-like equations , 1980 .

[28]  A. Majda,et al.  Absorbing boundary conditions for the numerical simulation of waves , 1977 .

[29]  E. Lindman.  “Free-space” boundary conditions for the time dependent wave equation , 1975 .

[30]  K. Yee.  Numerical solution of initial boundary value problems involving maxwell's equations in isotropic media , 1966 .

[31]  D. Katz,et al.  Validation and extension to three dimensions of the Berenger PML absorbing boundary condition for FD-TD meshes , 1994, IEEE Microwave and Guided Wave Letters.