By Costas D. Sarris
This monograph is a finished presentation of state of the art methodologies which could dramatically increase the potency of the finite-difference time-domain (FDTD) method, the most well-liked electromagnetic box solver of the time-domain kind of Maxwell's equations. those methodologies are aimed toward optimally tailoring the computational assets wanted for the wideband simulation of microwave and optical buildings to their geometry, in addition to the character of the sector ideas they aid. that's completed via the advance of strong ''adaptive meshing'' techniques, which quantity to various the complete variety of unknown box amounts throughout the simulation to evolve to temporally or spatially localized box gains. whereas mesh model is an incredibly fascinating FDTD function, recognized to lessen simulation occasions through orders of importance, it isn't constantly powerful. the categorical innovations provided during this publication are characterised through balance and robustness. hence, they're very good machine research and layout (CAD) instruments.
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Additional resources for Adaptive Mesh Refinement for Time-Domain Numerical Electromagnetics
As a result, a stable time step for the MRTD region is also stable for FDTD. 2 Connection Algorithm A simple, one-dimensional example of an interface between a first-order Haar MRTD and the corresponding FDTD scheme is shown in Fig. 13. For the update of the electric field ψ ψ ψ φ MRTD coefficients E5 , E5 , E5 10 , E5 11 , magnetic scaling and wavelet terms one cell to the left, within the FDTD region, are necessary. For their calculation, the FDTD nodal values of the magnetic field H1 , H2 , H3 , H4 are used as an input to a recursive fast wavelet transform (FWT).
This chapter presents an efficient implementation of thresholding applied to a nonlinear problem and reports significant execution time savings compared to the conventional FDTD technique, that the application of the proposed method has led to. 1 INTRODUCTION Multiresolution analysis (MRA) concepts have already been employed in a wide range of applications [11,14,15,37]. A motivating force for this research activity is the fact that wavelet-based methods provide the most natural framework for the implementation of adaptive grids, dynamically following local variations and singularities of solutions to partial differential equations.
A basis that has also been used in applications, is the cubic spline Battle–Lemarie basis . The Battle–Lemarie scaling and mother wavelet (Fig. 6) are entire domain functions and therefore schemes that are developed in this basis have to be truncated with respect to space. However, Battle–Lemarie scaling and wavelets have an excellent localization both in space and Fourier domains (Fig. 7), a feature that permits an a priori estimate of the necessary levels of resolution for correct field modeling.
Adaptive Mesh Refinement for Time-Domain Numerical Electromagnetics by Costas D. Sarris