On the accuracy of the ADI-FDTD method

We present an analytical study of the alternating-direction implicit finite-difference time-domain (ADI-FDTD) method for solving time-varying Maxwell's equations and compare its accuracy with that of the Crank-Nicolson (CN) and Yee FDTD schemes. The closed form of the truncation error is obtained for two and three dimensions. The dependence of the truncation error on the square of the time step multiplied by the spatial derivatives of the fields is found to be a unique feature of the ADI-FDTD scheme. We illustrate the limitation on accuracy imposed by these truncation error terms by simulating a simple parallel-plate structure excited by a low-frequency voltage source. Excellent agreement is obtained between field data computed with the implicit CN scheme using time steps greatly exceeding the Courant limit and field data computed with the explicit Yee scheme. Such results are not obtained with ADI-FDTD.

[1]  Sysi-Aho Marko,et al.  The Finite Difference Method in Partial Differential Equations , 2001 .

[2]  P. Vainikainen,et al.  A new heuristic diffraction coefficient for lossy dielectric wedges at normal incidence , 2002, IEEE Antennas and Wireless Propagation Letters.

[3]  J. J. Douglas.  On the Numerical Integration of $\frac{\partial ^2 u}{\partial x^2 } + \frac{\partial ^2 u}{\partial y^2 } = \frac{\partial u}{\partial t}$ by Implicit Methods , 1955 .

[4]  T. Namiki,et al.  Numerical simulation of microstrip resonators and filters using the ADI-FDTD method , 2001 .

[5]  Kai Virtanen,et al.  Manuscript received... , 2009 .

[6]  T. Namiki,et al.  Numerical simulation using ADI-FDTD method to estimate shielding effectiveness of thin conductive enclosures , 2001 .

[7]  Zhizhang Chen,et al.  A finite-difference time-domain method without the Courant stability conditions , 1999 .

[8]  T. Namiki,et al.  A new FDTD algorithm based on alternating-direction implicit method , 1999 .

[9]  김덕영.  [신간안내] Computational Electrodynamics (the finite difference time - domain method) , 2001 .

[10]  T. Namiki,et al.  Investigation of numerical errors of the two-dimensional ADI-FDTD method [for Maxwell's equations solution] , 2000 .

[11]  Zhizhang Chen,et al.  Numerical dispersion analysis of the unconditionally stable 3-D ADI-FDTD method , 2001 .

[12]  H. H. Rachford,et al.  The Numerical Solution of Parabolic and Elliptic Differential Equations , 1955 .

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