A split step approach for the 3-D Maxwell's equations

Lee, Jongwoo; Fornberg, Bengt

doi:10.1016/s0377-0427(03)00484-9

Cited by 167 publications

(114 citation statements)

References 14 publications

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“…LOD-FDTD is also divided into two substeps, similarly to ADI-FDTD [20], [22], [24]. However, for each time step, only two update equations are involved.…”

Section: B Lod-fdtdmentioning

confidence: 99%

“…This choice can be confirmed by deriving LOD-FDTD updates, using matrix operators [16] suitable for the Drude model. We write down governing (6)- (11) in the matrix form: (40) with and (41) Using the LOD-splitting technique, the two substep procedures of LOD-FDTD are written as [20], [24] (42) (43) with and a proper choice of and :…”

Section: B Lod-fdtdmentioning

confidence: 99%

“…Another unconditionally stable time-domain approach is based on the locally one-dimensional (LOD)-splitting technique [20]- [29], sometimes referred to as split-step technique [20], [21], [27]. This unconditionally stable FDTD technique yields a very simple algorithm, making it attractive for simulations involving frequency-dispersive media.…”

mentioning

confidence: 99%

“…In contrast to the ADI algorithm however, the LOD technique is only first-order accurate in time. This limitation can be circumvented by a modified Strang splitting, as suggested in [20] and [27] at the cost of an increase in the number of arithmetic operations. This latter technique is denoted here as LOD-FDTD with Strang splitting.…”

mentioning

confidence: 99%

See 3 more Smart Citations

A Study on Unconditionally Stable FDTD Methods for the Modeling of Metamaterials

Nascimento¹,

Jung

Borges

et al. 2009

J. Lightwave Technol.

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“…LOD-FDTD is also divided into two substeps, similarly to ADI-FDTD [20], [22], [24]. However, for each time step, only two update equations are involved.…”

Section: B Lod-fdtdmentioning

confidence: 99%

Section: B Lod-fdtdmentioning

confidence: 99%

mentioning

confidence: 99%

mentioning

confidence: 99%

See 2 more Smart Citations

A Study on Unconditionally Stable FDTD Methods for the Modeling of Metamaterials

Nascimento¹,

Jung

Borges

et al. 2009

J. Lightwave Technol.

View full text Add to dashboard Cite

show abstract

“…Recently, Zhang et al [21] further extended the artificial anisotropy revision method to higher order ADI-FDTD. Meanwhile, the split-step approach [22] and locally-one-dimensional (LOD) FDTD methods [23] were developed, of which the latter can be considered as a special case of the former. Later, high-order split-step FDTD methods in 2-D [24] and 3-D [25,26] were presented.…”

Section: Introductionmentioning

confidence: 99%

Reduction of Numerical Dispersion of Adi-FDTD Method With Quasi Isotropic Spatial Difference Scheme

Yi-long¹,

Su²,

Liu³

2013

PIER B

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Abstract-In this paper, the difference scheme of the alternatingdirection-implicit finite-difference time-domain (ADI-FDTD) method is replaced by the quasi isotropic (QI) spatial difference scheme to improve its numerical dispersion characteristics. The unconditional stability advantage of QI-ADI-FDTD is analytically proven and numerically verified. The numerical dispersion of the novel method can be dramatically reduced by choosing proper weighting factor. An example is simulated to demonstrate the accuracy and efficiency of the proposed method.

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Fast explicit operator splitting method for convection–diffusion equations

Chertock

Kurganov

Petrova

2006

Numerical Methods in Fluids

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SUMMARYSystems of convection-diffusion equations model a variety of physical phenomena which often occur in real life. Computing the solutions of these systems, especially in the convection dominated case, is an important and challenging problem that requires development of fast, reliable and accurate numerical methods. In this paper, we propose a second-order fast explicit operator splitting (FEOS) method based on the Strang splitting. The main idea of the method is to solve the parabolic problem via a discretization of the formula for the exact solution of the heat equation, which is realized using a conservative and accurate quadrature formula. The hyperbolic problem is solved by a second-order finite-volume Godunov-type scheme.We provide a theoretical estimate for the convergence rate in the case of one-dimensional systems of linear convection-diffusion equations with smooth initial data. Numerical convergence studies are performed for one-dimensional nonlinear problems as well as for linear convection-diffusion equations with both smooth and nonsmooth initial data. We finally apply the FEOS method to the one-and two-dimensional systems of convection-diffusion equations which model the polymer flooding process in enhanced oil recovery. Our results show that the FEOS method is capable to achieve a remarkable resolution and accuracy in a very efficient manner, that is, when only few splitting steps are performed.

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A split step approach for the 3-D Maxwell's equations

Cited by 167 publications

References 14 publications

A Study on Unconditionally Stable FDTD Methods for the Modeling of Metamaterials

A Study on Unconditionally Stable FDTD Methods for the Modeling of Metamaterials

Reduction of Numerical Dispersion of Adi-FDTD Method With Quasi Isotropic Spatial Difference Scheme

Fast explicit operator splitting method for convection–diffusion equations

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