2012•IEEE Transactions on Antennas and PropagationRequires access

An Unconditionally Stable One-Step Arbitrary-Order Leapfrog ADI-FDTD Method and Its Numerical Properties

Shunchuan Yang, Zhizhang Chen, Yiqiang Yu, Wen‐Yan Yin

Abstract

An one-step arbitrary-order leapfrog alternating-direction-implicit finite-difference time-domain (ADI-FDTD) method is presented. Its unconditional stability is analytically proven and numerically verified. Its numerical properties are shown to be identical to those of the conventional ADI-FDTD and LOD-FDTD methods. However, its computational expenditure is found to be the lowest. In other words, in comparison with the ADI-FDTD and LOD-FDTD methods, the one-step arbitrary-order leap-frog ADI-FDTD method retains identical numerical modeling accuracy but with higher computational efficiency.

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Key concepts: Finite-difference time-domain method, Alternating direction implicit method, Stability (learning theory), Mathematics, Numerical stability, Applied mathematics, Finite difference method, Numerical analysis