A Leapfrog Formulation of the 3D ADI-FDTD Algorithm
A Leapfrog Formulation of the 3D ADI-FDTD Algorithm
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DOI：
10.1109/cemtd.2007.4373546
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发表时间：
2007-10
期刊：
影响因子：
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通讯作者：
S. Cooke;M. Botton;T. Antonsen;B. Levush
中科院分区：
文献类型：
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作者：
S. Cooke;M. Botton;T. Antonsen;B. Levush
我们介绍了一种新的，替代形式的3D交替方向隐式时域有限差分（ADI- FDTD）算法，具有许多有吸引力的电磁模拟性能。我们得到了一个跳跃形式的时间推进方程，其中的E-和H-字段分别交错在半整数和整数的时间步长，保持了ADI-FDTD方法的无条件稳定性。得到的方程类似于显式蛙跳FDTD方法，但场更新方程被修改为包括在每一步的三对角方程组的解决方案，类似于原始的ADI- FDTD方案，使该方案不受Courant-Friedrichs-Lewy（CFL）限制。该算法比ADI-FDTD方法简单，但代数等价，允许减少计算，以实现相同的数值解。我们讨论了制定的优点，原来的FDTD和ADI-FDTD方法，并确认我们的结果数值。
We introduce a new, alternative form of the 3D alternating direction implicit finite-difference time-domain (ADI- FDTD) algorithm that has a number of attractive properties for electromagnetic simulation. We obtain a leapfrog form of the time advance equations, where the E- and H- fields are staggered at half-integer and integer time steps respectively, that preserves the unconditional stability of the ADI-FDTD method. The resulting equations resemble the explicit leapfrog FDTD method, but the field update equations are modified to include the solution of sets of tridiagonal equations at each step, similar to the original ADI- FDTD scheme, so that the scheme is not constrained by the Courant-Friedrichs-Lewy (CFL) limit. The algorithm is simpler than the ADI-FDTD method but algebraically equivalent, allowing a reduction in computation to achieve the same numerical solution. We discuss the advantages of the formulation over the original FDTD and ADI-FDTD methods, and confirm our results numerically.