High-Order Compact-Difference Schemes for Time-Dependent Maxwell Equations

Two high-order compact-difference schemes have been developed for solving three-dimensional, time-dependent Maxwell equations. Spurious high-frequency oscillatory components of the numerical solution, which are considered to be among the principal sources of time instability, are effectively suppressed by a spatial filter. The present numerical schemes are validated by calculations of three-dimensional transient electromagnetic waves within a waveguide, an oscillating electric dipole, and the radar cross section of perfectly electrical conducting sphere.

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

[2]  D. Gaitonde,et al.  Practical aspects of high-order accurate finite-volume schemes for electromagnetics , 1997 .

[3]  C. Tam,et al.  Dispersion-relation-preserving finite difference schemes for computational acoustics , 1993 .

[4]  Bertil Gustafsson,et al.  Fourth-order difference methods for hyperbolic IBVPs , 1995 .

[5]  Datta Gaitonde,et al.  High-order accurate methods for unsteady vortical flows on curvilinear meshes , 1998 .

[6]  J. S. Shang.  A fractional-step method for solving 3D, time-domain Maxwell equations , 1995 .

[7]  J. S. Shang,et al.  A Comparative Study of Characteristic-Based Algorithms for the Maxwell Equations , 1996 .

[8]  T. Senior,et al.  Electromagnetic and Acoustic Scattering by Simple Shapes , 1969 .

[9]  S. Lele.  Compact finite difference schemes with spectral-like resolution , 1992 .

[10]  R. Pletcher,et al.  Computational Fluid Mechanics and Heat Transfer. By D. A ANDERSON, J. C. TANNEHILL and R. H. PLETCHER. Hemisphere, 1984. 599 pp. $39.95. , 1986, Journal of Fluid Mechanics.

[11]  H. Kreiss,et al.  Stability Theory of Difference Approximations for Mixed Initial Boundary Value Problems. II , 1972 .

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

[13]  D. Gaitonde,et al.  High-order finite-volume schemes in wave propagation phenomena , 1996 .

[14]  Y. Adam,et al.  Highly accurate compact implicit methods and boundary conditions , 1977 .

[15]  J.S. Shang.  Challenges for computational electromagnetics in the time domain , 1997, IEEE Antennas and Propagation Society International Symposium 1997. Digest.

[16]  J. Bowles,et al.  Fourier Analysis of Numerical Approximations of Hyperbolic Equations , 1987 .

[17]  L. Collatz.  The numerical treatment of differential equations , 1961 .

[18]  Datta V. Gaitonde,et al.  Characteristic-based, time-dependent Maxwell equation solvers on a general curvilinear frame , 1995 .

[19]  D. Gottlieb,et al.  Time-stable boundary conditions for finite-difference schemes solving hyperbolic systems: methodology and application to high-order compact schemes , 1994 .

[20]  Andreas C. Cangellaris,et al.  A Reflectionless Sponge Layer Absorbing Boundary Condition for the Solution of Maxwell's Equations with High-Order Staggered Finite Difference Schemes , 1998 .

[21]  Jian-Ming Jin,et al.  Perfectly Matched Layers in the Discretized Space: An Analysis and Optimization , 1996 .

[22]  Datta V. Gaitonde,et al.  Optimized Compact-Difference-Based Finite-Volume Schemes for Linear Wave Phenomena , 1997 .

[23]  D. Gottlieb,et al.  The Stability of Numerical Boundary Treatments for Compact High-Order Finite-Difference Schemes , 1993 .

[24]  B. Gustafsson.  The convergence rate for difference approximations to mixed initial boundary value problems , 1975 .