The Huygens subgridding for the numerical solution of the Maxwell equations

The Huygens subgridding (HSG) is a subgridding technique developed for the numerical solution of the Maxwell equations. It relies on the theoretical equivalence of any physical volume with two or more fictitious volumes connected by equivalent currents. The application of this concept to the finite-difference time-domain (FDTD) method has been previously published in the one dimensional and two dimensional cases. In this paper the HSG is extended to the general three dimensional case, the exchange of the electromagnetic energy between the two FDTD grids is investigated theoretically, and some modifications to the HSG algorithm are presented with the objective of simplifying its implementation.

[1]  M. Okoniewski,et al.  Three-dimensional subgridding algorithm for FDTD , 1997 .

[2]  R. Lee,et al.  Optimization of subgridding schemes for FDTD , 2002, IEEE Microwave and Wireless Components Letters.

[3]  G. Pan,et al.  A novel subgridding technique for unconditionally stable time domain method , 2010, IEEE Antennas and Propagation Society International Symposium.

[4]  K. Kunz,et al.  Finite-Difference Analysis of EMP Coupling to Lossy Dielectric Structures , 1980, IEEE Transactions on Electromagnetic Compatibility.

[5]  Thomas Weiland,et al.  A CONSISTENT SUBGRIDDING SCHEME FOR THE FINITE DIFFERENCE TIME DOMAIN METHOD , 1996 .

[6]  L. Cristoforetti,et al.  A robust and efficient subgridding algorithm for finite-difference time-domain simulations of Maxwell's equations , 2004 .

[7]  S. A. Schelkunoff,et al.  Some equivalence theorems of electromagnetics and their application to radiation problems , 1936 .

[8]  R. Lee,et al.  Conservative and Provably Stable FDTD Subgridding , 2007, IEEE Transactions on Antennas and Propagation.

[9]  J.-P. Wrenger,et al.  Numerical reflection from FDTD-PMLs: a comparison of the split PML with the unsplit and CFS PMLs , 2002 .

[10]  Allen Taflove,et al.  A Novel Method to Analyze Electromagnetic Scattering of Complex Objects , 1982, IEEE Transactions on Electromagnetic Compatibility.

[11]  V. P. Cable,et al.  FDTD local grid with material traverse , 1997 .

[12]  F. Costen,et al.  Application of huygens subgridding technique to human body modelling , 2008, 2008 IEEE Antennas and Propagation Society International Symposium.

[13]  K. Yee,et al.  A subgridding method for the time-domain finite-difference method to solve Maxwell's equations , 1991 .

[14]  Zhizhang David Chen,et al.  A hybrid ADI-FDTD subgridding scheme for efficient electromagnetic computation: Research Articles , 2004 .

[15]  John B. Schneider,et al.  FDTD dispersion revisited: faster-than-light propagation , 1999 .

[16]  F. Teixeira,et al.  Improved FDTD subgridding algorithms via digital filtering and domain overriding , 2005, IEEE Transactions on Antennas and Propagation.

[17]  J. Bérenger.  A Huygens Subgridding for the FDTD Method , 2006, IEEE Transactions on Antennas and Propagation.

[18]  B. Donderici,et al.  Domain-overriding and digital filtering for 3-D FDTD subgridded simulations , 2006, IEEE Microwave and Wireless Components Letters.

[19]  A new stable hybrid three-dimensional generalized finite difference time domain algorithm for analyzing complex structures , 2005, IEEE Transactions on Antennas and Propagation.

[20]  Jean-Pierre Berenger,et al.  Evanescent waves in PML's: origin of the numerical reflection in wave-structure interaction problems , 1999 .

[21]  T. Fouquet,et al.  Conservative space-time mesh refinement methods for the FDTD solution of Maxwell's equations , 2006 .

[22]  Raj Mittra,et al.  A NEW SUBGRIDDING METHOD FOR THE FINITE-DIFFERENCE TIME-DOMAIN (FDTD) ALGORITHM , 1999 .

[23]  Jean-Pierre Berenger.  Making use of the PML absorbing boundary condition in coupling and scattering FDTD computer codes , 2003 .

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

[25]  Zhizhang Chen,et al.  A hybrid ADI‐FDTD subgridding scheme for efficient electromagnetic computation , 2004 .

[26]  Y. Gan,et al.  A Stable FDTD Subgridding Method Based on Finite Element Formulation With Hanging Variables , 2007, IEEE Transactions on Antennas and Propagation.

[27]  I. S. Kim,et al.  A local mesh refinement algorithm for the time domain-finite difference method using Maxwell's curl equations , 1990 .

[28]  Ryan Austin Chilton,et al.  H-, P- and T-Refinement Strategies for the Finite-Difference-Time-Domain (FDTD) Method Developed via Finite-Element (FE) Principles , 2008 .

[29]  N. Shuley,et al.  A method for incorporating different sized cells into the finite-difference time-domain analysis technique , 1992, IEEE Microwave and Guided Wave Letters.

[30]  J. Bérenger,et al.  Extension of the FDTD Huygens Subgridding Algorithm to Two Dimensions , 2009, IEEE Transactions on Antennas and Propagation.