Nonstandard and Higher-Order Finite-Difference Methods for Electromagnetics
Final rept. 1 Jul 2005-30 Jun 2009
ARIZONA STATE UNIV TEMPE DEPT OF ELECTRICAL ENGINEERING
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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 Gausss 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.
- Theoretical Mathematics
- Electricity and Magnetism
- Radiofrequency Wave Propagation