Dispersion-relation-preserving finite difference schemes for computational acoustics
Journal of Computational Physics
High-Accuracy Finite-Difference Schemes for Linear Wave Propagation
SIAM Journal on Scientific Computing
On the construction of a high order difference scheme for complex domains in a Cartesian grid
Proceedings of the fourth international conference on Spectral and high order methods (ICOSAHOM 1998)
Fourth order compact implicit method for the Maxwell equations with discontinuous coefficients
Proceedings of the fourth international conference on Spectral and high order methods (ICOSAHOM 1998)
An explicit fourth-order staggered finite-difference time-domain method for Maxwell's equations
Journal of Computational and Applied Mathematics
International Journal of Numerical Modelling: Electronic Networks, Devices and Fields
Finite difference time domain dispersion reduction schemes
Journal of Computational Physics
International Journal of RF and Microwave Computer-Aided Engineering
Optimization, resolution and application of composite compact finite difference templates
Applied Numerical Mathematics
An FDTD scheme on a face-centered-cubic (FCC) grid for the solution of the wave equation
Journal of Computational Physics
Fourth-order finite-difference time-domain method based on error-controlling concepts
International Journal of Numerical Modelling: Electronic Networks, Devices and Fields
Hi-index | 31.46 |
We define a new concept, termed the spectral order of accuracy (SOoA), which is the spectral domain analogue of the familiar order of accuracy (OoA). The SOoA is pivotal in a refined version of a recently-introduced methodology for formulating excitation-adaptive wave equation FDTD (WE-FDTD) schemes, described below. This concept is the basis for a unified classification for both existing and new schemes. Both one- and two-dimensional cases are presented for boundless, source free, homogeneous, isotropic and lossless media. The 1-D and 2-D cases are developed in detail for the (3,2M+1) (temporal, spatial) and (3,3) 2-D stencils, respectively. Stability analysis is built into the methodology in terms of either analytical conditions or ''stability maps'' defined herein. The methodology is seen as a generalization of many existing schemes that also provides a unified tool for a systematical design of WE-FDTD schemes subject to specific requirements in terms of the spectral content of the excitation. The computational efficiency for all schemes remains the same for a given stencil, since the core of the FDTD code is unchanged between schemes, the difference being only in the values of scheme coefficients.