An FDTD scheme on a face-centered-cubic (FCC) grid for the solution of the wave equation

Potter, M. E.; Lamoureux, Michael P.; Nauta, M. D.

doi:10.1016/j.jcp.2011.04.027

Cited by 23 publications

(10 citation statements)

References 16 publications

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“…2b for Heaviside's load corresponds to the analytical solution (see [44]) asymptotically valid in the vicinity of the front…”

Section: Longitudinal Waves In a Thin Rod Embedded Into Elastic Mediummentioning

confidence: 98%

“…In the present decade, the problem under study has become topical again due to the development of FDTM (Finite-Difference Time-Domain Method) of calculation of electromagnetic waves propagation [39]. This method was adapted to the calculation of geophysical and geodynamic problems in [40][41][42][43][44]. Here the attention was mainly focused on the construction of various grid stencils allowing to obtain an acceptably exact solution within the class of smooth functions.…”

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confidence: 99%

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Numerical simulation of shock-wave processes in elastic media and structures. Part I: Solving method and algorithms

et al. 2012

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Finite-difference algorithms for solving non-stationary wave problems are presented, which allow to obtain the description of fronts and front zones with a minimal influence of spurious effects of numerical approximation. The principal condition of the construction of calculation algorithms is the convergence of domains of dependence of continual and difference equations. It is shown that the fulfillment of this condition provides a maximally exact wave fronts description. Numerical solutions of several one-dimensional and two-dimensional wave problems are presented. In the second part of the paper, we will give examples of numerical simulation of applied problems of structure dynamics and geodynamics -impact driving of piles into the soil, formation of pendulum waves in a block massif, stress state of a homogeneous massif in the zone of interaction with a punch, fracture of a layered solid under the action of a local pulse, and high-speed penetration of a layered target.Exact calculation of wave fronts and high-frequency disturbances is always of utmost importance for problems of numerical simulation of the dynamics of deformable media and structures. On the one hand, this is due to an attempt to expand the base of test problems formed by analytical solutions, which is an essential aspect of numerical simulation. On the other hand, it is important for the analysis of various applied problems having no analytical solutions, in which the parameters of wave fronts and disturbances in their vicinity may be criterial for the strength and shock resistance estimation. Examples of such problems in mining are shock pulses propagation in block media, dynamic strength of component parts of impact machines, stability of underground structures under explosions and rock bursts, etc. Adequate simulation of discontinuous and high-frequency components of the wave field acquires special importance due to multiple reflections of unit waves from inhomogeneities that are inevitably present in actual media and structures.Apart from scarce and relatively simple models of the dynamics of media and structures, wave processes in structured bodies cannot be described using analytical approaches.Undoubtedly, the idea of adequate numerical simulation of a wave field with discontinuities in inhomogeneous media and compound structures is attractive. Numerical solutions not only essentially supplement the known analytical ones, but also allow to obtain qualitative and quantitative evaluations of the process under study and to explain physical consequences. Besides, numerical

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“…2b for Heaviside's load corresponds to the analytical solution (see [44]) asymptotically valid in the vicinity of the front…”

Section: Longitudinal Waves In a Thin Rod Embedded Into Elastic Mediummentioning

confidence: 98%

mentioning

confidence: 99%

Numerical simulation of shock-wave processes in elastic media and structures. Part I: Solving method and algorithms

et al. 2012

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“…Acoustic wave satisfies the Hooke's Law which relates the stress (tensor) and strain (force) of the waveguiding materials [23][24][25][26][27].…”

Section: B Acoustic Modesmentioning

confidence: 99%

Evolution of Surface Acoustic Waves in an Optical Microfiber

Emami

Lee

Rahman

et al. 2017

IEEE J. Quantum Electron.

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This is the accepted version of the paper.This version of the publication may differ from the final published version. 1  Abstract-This paper reports SBS characterization in a tapered optical fiber using full-vectorial finite element based numerical methods. Numerical simulations of both optical and acoustic waves' propagation through a tapered microfiber have been carried out. Acoustic modes over a range of wavenumber for different fiber core radii are obtained and nature of their both dominant and non-dominant displacement vector profiles are studied and discussed. Acoustic mode profiles show confinement of the acoustic wave predominantly at the core cladding interface. In addition, the acousto-optical overlap factors at different fiber radii are also presented. Permanent

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“…Recently in [15] we reported on the use of the FCC structure to develop an FDTD method for the scalar wave equation. The dispersion and stability of the method were analyzed and compared with an equivalent Cartesian method, and it was shown that not only is the isotropy greatly improved, but the stability criterion is also relaxed.…”

Section: Introductionmentioning

confidence: 99%

“…Section II outlines the geometry of the FCC grid structure, and develops the update equa-0018-926X/$31.00 © 2012 IEEE tions for the new FDTD method. Section III highlights the dispersion equation (which is exactly the same as in [15]) and stability criterion, and compares this with the standard Yee method. Section IV provides numerical examples to provide evidence of the improved isotropy, followed by conclusions.…”

Section: Introductionmentioning

confidence: 99%

FDTD on Face-Centered Cubic (FCC) Grids for Maxwell's Equations

Potter

Nauta

2013

IEEE Trans. Antennas Propagat.

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The standard FDTD method for Maxwell's equations is reformulated on face-centered cubic (FCC) grids as an alternative to the standard Cartesian (Yee) grid. Dispersion and stability for the formulation are also presented, and a comparison is made with the standard FDTD formulation using the metric of equal volume density of gridpoints. Although the new formulation has four times as many lattice points per unit voxel in comparison with the standard formulation, the new formulation shows much better grid isotropy. Furthermore, the new formulation has a stability criterion that is approximately 1.4 times more relaxed than that of the standard formulation.Index Terms-Finite difference methods, FDTD methods, numerical dispersion.

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An FDTD scheme on a face-centered-cubic (FCC) grid for the solution of the wave equation

Cited by 23 publications

References 16 publications

Numerical simulation of shock-wave processes in elastic media and structures. Part I: Solving method and algorithms

Numerical simulation of shock-wave processes in elastic media and structures. Part I: Solving method and algorithms

Evolution of Surface Acoustic Waves in an Optical Microfiber

FDTD on Face-Centered Cubic (FCC) Grids for Maxwell's Equations

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