Low-Dispersion Algorithms Based on the Higher Order

Zygiridis, Theodoros T.; Tsiboukis, T.D.

doi:10.1109/tmtt.2004.825695

Cited by 63 publications

(37 citation statements)

References 17 publications

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“…Given the desired level of accuracy, the minimum grid densities Maximum L 2 (t) error (4,4) required to satisfy this threshold, as well as the respective simulation times, are determined for all schemes. In addition, we consider the performance of two other reduced-dispersion techniques, proposed in the past: the (2, 4) method incorporating artificially anisotropic materials [23], and a narrowband technique, which encompasses modified spatial and temporal expressions in a (2, 4) computational stencil [24]. The obtained results are exhibited in Fig.…”

Section: Numerical Resultsmentioning

confidence: 99%

“…The incorporation of the second-order time-stepping renders the fourth-order spatial approximations practically useless, unless very fine temporal increments are selected (a solution with high computational cost). In fact, we have shown in [24] alternative ways to significantly improve the accuracy of the (2, 4) approach close to the stability limit, by sacrificing the formal accuracy and retaining the spatial stencil.…”

Section: Motivation For the Development Of Novel Fdtd Schemesmentioning

confidence: 99%

See 1 more Smart Citation

Optimized three-dimensional FDTD discretizations of Maxwell’s equations on Cartesian grids

Zygiridis¹,

Tsiboukis²

2007

Journal of Computational Physics

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Section: Numerical Resultsmentioning

confidence: 99%

Section: Motivation For the Development Of Novel Fdtd Schemesmentioning

confidence: 99%

Optimized three-dimensional FDTD discretizations of Maxwell’s equations on Cartesian grids

Zygiridis¹,

Tsiboukis²

2007

Journal of Computational Physics

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“…An optimized central difference format was proposed to reduce numerical dispersion in [16,17], where the second-order precision central difference format with the general form at point i in space is expressed as ∂f (t; x, y, z) ∂u…”

Section: Methodsmentioning

confidence: 99%

“…An optimized difference item which is from transform domain to achieve the approximation of partial differential operator is presented in [16,17]. It has been demonstrated that the optimized difference item can effectively reduce the numerical dispersion compared with conventional central difference item which is meaningful for model of wave propagation in dispersive medium using FDTD method [18].…”

Section: Introductionmentioning

confidence: 99%

An Optimized PLRC-FDTD Model of Wave Propagation in Anisotropic Magnetized Plasma

Ding¹,

Zhao²,

Yang³

et al. 2017

PIER M

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Abstract-Numerical dispersion is the main error source of the finite-difference time-domain (FDTD) method. In this paper, an optimized piecewise linear recursive convolution (PLRC) FDTD method with low numerical dispersion is presented first time for electromagnetic-wave propagation in anisotropic magnetized plasma. An optimized difference item which can achieve better approximation to the partial differential operator from transform domain is induced in this algorithm which decreases numerical dispersion. The item can be regarded as adding a correcting coefficient to conventional central difference format. And it is easy for programming and implementation. Numerical examples of electromagnetic pulse wave propagating in plasma demonstrate that the proposed optimized PLRC-FDTD method can not only reduce the numerical dispersion, but also improve precision, saving computational memory and computational time compared with the conventional PLRC-FDTD method. Same accuracy can be achieved when the spatial mesh size for the optimized PLRC-FDTD method is 2 times coarser as that in the conventional PLRC-FDTD method, corresponding to the computation time consumed in the optimized method is only 1/2 as that in the conventional one.

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“…An alternative is thus to look for FDTD-like methods (preserving low computational costs) but with high order (to lower dispersion error). The two main ways were thus to develop finite differences on bigger stencils [3] [4], or introduce polynomial basis functions in cells [5] [6].…”

Section: Introductionmentioning

confidence: 99%

New high order FDTD method to solve EMC problems

Deymier¹,

Volpert²,

Ferrières³

et al. 2015

AEM

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In electromagnetic compatibility (EMC) context, we are interested in developing new accurate methods to solve efficiently and accurately Maxwell's equations in the time domain. Indeed, usual methods such as FDTD or FVTD present important dissipative and/or dispersive errors which prevent to obtain a good numerical approximation of the physical solution for a given industrial scene unless we use a mesh with a very small cell size. To avoid this problem, schemes like the Discontinuous Galerkin (DG) method, based on higher order spatial approximations, have been introduced and studied on unstructured meshes. However the cost of this kind of method can become prohibitive according to the mesh used. In this paper, we first present a higher order spatial approximation method on cartesian meshes. It is based on a finite element approach and recovers at the order 1 the well-known Yee's scheme. Next, to deal with EMC problem, a nonoriented thin wire formalism is proposed for this method. Finally, several examples are given to present the benefits of this new method by comparison with both Yee's scheme and DG approaches.

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Low-Dispersion Algorithms Based on the Higher Order

Cited by 63 publications

References 17 publications

Optimized three-dimensional FDTD discretizations of Maxwell’s equations on Cartesian grids

Optimized three-dimensional FDTD discretizations of Maxwell’s equations on Cartesian grids

An Optimized PLRC-FDTD Model of Wave Propagation in Anisotropic Magnetized Plasma

New high order FDTD method to solve EMC problems

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