Finite difference time domain dispersion reduction schemes

Finkelstein, B.; Kästner, R.

doi:10.1016/j.jcp.2006.06.016

Cited by 129 publications

(57 citation statements)

References 39 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…They showed that almost all the schemes using high-order finite difference provide substantial improvement in the dispersion errors compared with the classical Yee algorithm. Finkelstein and Kastner [17] presented a methodology for deriving a dispersion reduction scheme based on modifications of the characteristic equation for electromagnetic wave propagation problems.…”

Section: Introductionmentioning

confidence: 99%

Time-filtered leapfrog integration of Maxwell equations using unstaggered temporal grids

Mahalov

Moustaoui

2016

Journal of Computational Physics

View full text Add to dashboard Cite

A finite-difference time-domain method for integration of Maxwell equations is presented. The computational algorithm is based on the leapfrog time stepping scheme with unstaggered temporal grids. It uses a fourth-order implicit time filter that reduces computational modes and fourth-order finite difference approximations for spatial derivatives. The method can be applied within both staggered and collocated spatial grids. It has the advantage of allowing explicit treatment of terms involving electric current density and application of selective numerical smoothing which can be used to smooth out errors generated by finite differencing. In addition, the method does not require iteration of the electric constitutive relation in nonlinear electromagnetic propagation problems. The numerical method is shown to be effective and stable when employed within Perfectly Matched Layers (PML). Stability analysis demonstrates that the proposed method is effective in stabilizing and controlling numerical instabilities of computational modes arising in wave propagation problems with physical damping and artificial smoothing terms while maintaining higher accuracy for the physical modes. Comparison of simulation results obtained from the proposed method and those computed by the classical time filtered leapfrog, where Maxwell equations are integrated for a lossy medium, within PML regions and for Kerr-nonlinear media show that the proposed method is robust and accurate. The performance of the computational algorithm is also verified by analyzing parametric four wave mixing in an optical nonlinear Kerr medium. The algorithm is found to accurately predict frequencies and amplitudes of nonlinearly converted waves under realistic conditions proposed in the literature.

show abstract

Section: Introductionmentioning

confidence: 99%

Time-filtered leapfrog integration of Maxwell equations using unstaggered temporal grids

Mahalov

Moustaoui

2016

Journal of Computational Physics

View full text Add to dashboard Cite

show abstract

“…To improve the accuracy of FD 4 schemes for solving wave equations, many variants of the difference schemes have been 5 advanced, including staggered-grid (e.g. [10][11][12][13][14]), irregular grid (e.g. [15][16][17]), high-order 6 operator (e.g.…”

Section: Introductionmentioning

confidence: 99%

“…The trigonometric functions of dispersion relation are expanded into 13 polynomials by using TE to obtain the finite-difference coefficients. However, it just leads to 14 great accuracy at small wavenumbers for wave equation modeling. When seismic 15 wavenumber range is relatively larger, strong numerical dispersion will occur, resulting in 16 reducing the numerical accuracy [49].…”

Section: Introductionmentioning

confidence: 99%

Optimal staggered-grid finite-difference schemes by combining Taylor-series expansion and sampling approximation for wave equation modeling

Yan

Yang

2016

Journal of Computational Physics

View full text Add to dashboard Cite

“…Tessmer [16] discussed Seismic finite difference modeling with spatially variable time steps. Finkelstein et al [17] developed finite difference time domain dispersion reduction schemes. Y. Liu et al [18,19] discussed advanced and truncated finite difference method for seismic modeling and Y. Liu et al [20] employed a plane wave theory and the Taylor series expansion of dispersion relation to derive the FD coefficients in the joint time-space domain for the scalar wave equation with second-order spatial derivatives.…”

Section: Introductionmentioning

confidence: 99%

Modeling of Surface Waves in a Fluid Saturated Poro-Elastic Medium under Initial Stress Using Time-Space Domain Higher Order Finite Difference Method

Ghorai¹,

Tiwary²

2013

View full text Add to dashboard Cite

In this present context, mathematical modeling of the propagation of surface waves in a fluid saturated poro-elastic medium under the influence of initial stress has been considered using time dependent higher order finite difference method (FDM). We have proved that the accuracy of this finite-difference scheme is 2M when we use 2nd order time domain finite-difference and 2M-th order space domain finite-difference. It also has been shown that the dispersion curves of Love waves are less dispersed for higher order FDM than of lower order FDM. The effect of initial stress, porosity and anisotropy of the layer in the propagation of Love waves has been studied here. The numerical results have been shown graphically. As a particular case, the phase velocity in a non porous elastic solid layer derived in this paper is in perfect agreement with that of .

show abstract

Finite difference time domain dispersion reduction schemes

Cited by 129 publications

References 39 publications

Time-filtered leapfrog integration of Maxwell equations using unstaggered temporal grids

Time-filtered leapfrog integration of Maxwell equations using unstaggered temporal grids

Optimal staggered-grid finite-difference schemes by combining Taylor-series expansion and sampling approximation for wave equation modeling

Modeling of Surface Waves in a Fluid Saturated Poro-Elastic Medium under Initial Stress Using Time-Space Domain Higher Order Finite Difference Method

Contact Info

Product

Resources

About