Tensor product derivative matching for wave propagation in inhomogeneous media

We propose a tensor product derivative matching (TPDM) method to restore the accuracy of high-order finite difference time-domain (FDTD) schemes of computational electromagnetics (CEM) with material interfaces in two spatial dimensions (2D). By making use of fictitious points, the TPDM method locally enforces the physical-jump conditions at material interfaces in a preprocessing stage to arbitrarily high orders of accuracy in principle, based on a structured grid. The proposed method encompasses a variety of schemes of different orders in a single code. In fact, numerical orders from 2 to near 16 are confirmed in the present study. To the best of our knowledge, such high orders have not been reported in the literature for CEM problems involving material interfaces. The limitation and applicability of the present scheme are also analyzed in detail. © 2004 Wiley Periodicals, Inc. Microwave Opt Technol Lett 43: 69–77, 2004; Published online in Wiley InterScience (www.interscience.wiley.com). DOI 10.1002/mop.20378

[1]  P. Toulios,et al.  Fields in the focal region of offset parabolic antennas , 1976 .

[2]  Bo Zhang,et al.  An explicit fourth-order staggered finite-difference time-domain method for Maxwell's equations , 2002 .

[3]  David W. Zingg,et al.  High-Accuracy Finite-Difference Schemes for Linear Wave Propagation , 1996, SIAM J. Sci. Comput..

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

[5]  Tobin A. Driscoll,et al.  Block Pseudospectral Methods for Maxwell's Equations II: Two-Dimensional, Discontinuous-Coefficient Case , 1999, SIAM J. Sci. Comput..

[6]  Shan Zhao,et al.  Numerical solution of the Helmholtz equation with high wavenumbers , 2004 .

[7]  Amir Yefet,et al.  A staggered fourth-order accurate explicit finite difference scheme for the time-domain Maxwell's equations , 2001 .

[8]  Tobin A. Driscoll,et al.  A Block Pseudospectral Method for Maxwell's Equations , 1998 .

[9]  Shan Zhao,et al.  DSC time-domain solution of Maxwell's equations , 2003 .

[10]  Wei Cai,et al.  An upwinding embedded boundary method for Maxwell's equations in media with material interfaces: 2D case , 2003 .

[11]  Shan Zhao,et al.  High-order FDTD methods via derivative matching for Maxwell's equations with material interfaces , 2004 .

[12]  K. S. Yee,et al.  Conformal finite-different time-domain (FDTD) with overlapping grids , 1992 .

[13]  Allen Taflove,et al.  Finite-difference time-domain modeling of curved surfaces (EM scattering) , 1992 .

[14]  Shan Zhao,et al.  Local spectral time-domain method for electromagnetic wave propagation. , 2003, Optics letters.

[15]  Chi Hou Chan,et al.  An explicit fourth-order orthogonal curvilinear staggered-grid FDTD method for Maxwell's equations , 2002 .

[16]  J. Hesthaven,et al.  Convergent Cartesian Grid Methods for Maxwell's Equations in Complex Geometries , 2001 .

[17]  Eli Turkel,et al.  Fourth order compact implicit method for the Maxwell equations with discontinuous coefficients , 2000 .

[18]  Jan S. Hesthaven,et al.  High-order accurate methods in time-domain computational electromagnetics: A review , 2003 .

[19]  Peter G. Petropoulos,et al.  Phase error control for FD-TD methods of second and fourth order accuracy , 1994 .

[20]  Zhongxiang Shen,et al.  A generalized higher order finite-difference time-domain method and its application in guided-wave problems , 2003 .

[21]  A. Yefet,et al.  A non-dissipative staggered fourth-order accurate explicit finite difference scheme for the time-domain Maxwell''s equations , 1999 .

[22]  Eli Turkel,et al.  On the construction of a high order difference scheme for complex domains in a Cartesian grid , 2000 .

[23]  Jeffrey L. Young,et al.  Toward the construction of a fourth-order difference scheme for transient EM wave simulation: staggered grid approach , 1997 .

[24]  Qing Huo Liu,et al.  The PSTD algorithm: A time-domain method requiring only two cells per wavelength , 1997 .

[25]  R. Holland.  Finite-Difference Solution of Maxwell's Equations in Generalized Nonorthogonal Coordinates , 1983, IEEE Transactions on Nuclear Science.

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

[27]  Debiao Ge,et al.  Comparison study of the PSTD and FDTD methods for scattering analysis , 2000 .

[28]  K. S. Yee,et al.  Conformal finite difference time domain (FDTD) with overlapping grids , 1992, IEEE Antennas and Propagation Society International Symposium 1992 Digest.