Nonstandard and Higher-Order Finite-Difference Methods for Electromagnetics
Abstract
The major objective of this dissertation is to design simple low-dispersion Finite-Difference Time-Domain (FDTD) methods for electromagnetics. Literature review indicated that the Nonstandard Finite Difference (NSFD) method exhibits great potentials in dispersion reduction. Different from the Standard Finite Difference (SFD) methods, the NSFD methods are derived directly based upon dispersion analysis. In this dissertation, the basic concepts of the NSFD methods are generalized to various extended finite-difference stencils. Furthermore, several improved NSFD Numerical simulations show that these schemes significantly reduce the dispersion error of their standard counterparts. Many technical issues in practical implementations, such as absorbing boundary conditions, stability conditions, and Gauss's Laws, are discussed and justified. Moreover, two special conditions are proposed for the extended stencils in the vicinity of the dielectric material discontinuities. It was demonstrated that the accuracy of the fourth-order stencil is fully restored by applying these conditions.
Document Details
- Document Type
- Technical Report
- Publication Date
- Oct 26, 2009
- Accession Number
- ADA517572
Entities
People
- Bo Yang
- Constantine A. Balanis
- Craig R. Birtcher
Organizations
- Arizona State University