Efficient implicit FDTD algorithm based on locally one-dimensional scheme

By J. Shibayama, M. Muraki, J. Yamauchi, H. Nakano. 2005

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Time-Domain Finite-Difference and Finite-Element Methods for Maxwell Equations in Complex Media (2008, background): “on operator splitting such as the alternating-direction-implicit (ADI) scheme [310]–[313] and the locally-one-dimensional (LOD) scheme [314]–[316] have attracted much interest in recent years.”
Unconditionally Stable LOD–FDTD Method for 3-D Maxwell's Equations (2007, methodology): “Like the previous LOD–FDTD methods [6], [7], there are two updating proce-”
Development of the Three-Dimensional Unconditionally Stable LOD-FDTD Method (2008, methodology): “[16] O. Ramadan, “Unsplit field implicit PML algorithm for complex envelope dispersive LOD-FDTD simulations,” Electron.”
Explicit Time-Domain Finite-Element Method Stabilized for an Arbitrarily Large Time Step (2012, methodology): “In the FDTD based methods, a family of implicit schemes [1]–[9] such as the ADI (alternating direction implicit)-FDTD [1]–[3], the CN (Crank–Nicolson)-FDTD [4], the LOD (locally 1-D)-FDTD [5], the Laguerre-FDTD [6], and the split-step FDTD [8] methods have been developed to achieve unconditional sta”