By Costas D. Sarris
This monograph is a finished presentation of state of the art methodologies which could dramatically improve the potency of the finite-difference time-domain (FDTD) strategy, the preferred electromagnetic box solver of the time-domain type of Maxwell's equations. those methodologies are geared toward optimally tailoring the computational assets wanted for the wideband simulation of microwave and optical constructions to their geometry, in addition to the character of the sphere strategies they aid. that's completed via the advance of strong ''adaptive meshing'' techniques, which quantity to various the entire variety of unknown box amounts through the simulation to conform to temporally or spatially localized box positive aspects. whereas mesh model is an incredibly fascinating FDTD characteristic, recognized to minimize simulation instances via orders of value, it isn't regularly strong. the categorical suggestions awarded during this ebook are characterised via balance and robustness. accordingly, they're very good computing device research and layout (CAD) instruments.
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Additional info for Adaptive Mesh Refinement for Time-Domain Numerical Electromagnetics
Cls December 15, 2006 7:45 47 CHAPTER 3 Efficient Implementation of Adaptive Mesh Refinement in the Haar Wavelet-based MRTD Technique The main attractive feature of wavelet-based, time-domain techniques is the simple implementation of adaptive meshing, through the application of a thresholding procedure to eliminate wavelet coefficients that attain relatively insignificant values, at a limited compromise of accuracy. However, little attention has been devoted so far to the investigation of computational costs and accuracy trade-offs in order to obtain thresholding-related operation savings.
33), which in this case yields an offset of one quarter of a cell (Fig. 12), the equivalent grid points are leap-frogged in space and correctly correspond to the mesh of an FDTD scheme of cell size x/2. As discussed in , this latter approach leads to MRTD schemes with consistent numerical dispersion properties (as opposed to the former approach) and therefore, it is adopted in the following derivations. Upon substitution of the MRTD expansions of all field components into Eq. 28), Galerkin’s method is applied for the derivation of field update equations.
31). This argument is demonstrated for a zero-order Haar MRTD scheme, utilizing Haar scaling and zero-order wavelet functions (Fig. 3), in Fig. 12, which depict the equivalent grid points that are generated in both cases, in one dimension. 5)/2r x,max +1 x, with p = 0, 1 · · · 2r x,max +1 − 1. 11: Electric/magnetic field equivalent grid points for zero-order Haar MRTD in one dimension, under the common convention of half a cell offset between electric/magnetic scaling cells for the approximation of x-partial derivatives involved in Ey -updates).
Adaptive Mesh Refinement for Time-Domain Numerical Electromagnetics by Costas D. Sarris