On the Efficient and Accurate Application of Partial Differential Equation Solvers of Maxwell's Equations in the Time Domain
Aoyagi, Paul Hiroshi
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https://hdl.handle.net/2142/71973
Description
Title
On the Efficient and Accurate Application of Partial Differential Equation Solvers of Maxwell's Equations in the Time Domain
Author(s)
Aoyagi, Paul Hiroshi
Issue Date
1992
Doctoral Committee Chair(s)
Mittra, Raj
Department of Study
Electrical Engineering
Discipline
Electrical Engineering
Degree Granting Institution
University of Illinois at Urbana-Champaign
Degree Name
Ph.D.
Degree Level
Dissertation
Keyword(s)
Mathematics
Engineering, Electronics and Electrical
Physics, Acoustics
Abstract
A new field/voltage relation for use with the symmetric condensed node transmission line matrix (TLM) method is introduced. It is found that there is no rigorous mathematical proof which demonstrates the consistency and convergence of the symmetric condensed node TLM method under the field/voltage relation originally introduced. It is proposed that other field/voltage relations may exist which may be more consistent with Maxwell's equations and more accurate than the previous relation. The new field/voltage relation given is derived qualitatively by comparing the symmetric condensed node TLM algorithm with the Yee algorithm. It is demonstrated numerically that this new relation eliminates nonphysical spurious oscillations introduced by the conventionally used field/voltage relation near the source region.
The presence, cause and correction of a dc anomaly generated by modeling time limited sources using the Yee algorithm are discussed. It is shown mathematically that the Yee algorithm will preserve the divergence relation at any given time, t$\sb0$, for all time t $>$ t$\sb0$. It is demonstrated that this will result in the presence of fictitious static charges in the system even after charges have been removed from the system.
The optimum time step with which to operate the Yee algorithm is given. It is found that the Yee algorithm in unbounded space will be the most accurate when the discretization is fine enough and the simulations are run at the largest time step rather than at the smallest time step allowed by the CFL stability criterion.
A higher-order explicit differencing scheme of Maxwell's equation is considered. In particular, a second order accurate in time and fourth order accurate in space differencing scheme, i.e., 2-4 scheme, using central differencing is studied using Fourier analysis. The stability criterion for the 2-4 scheme is derived as well as expressions for the discretization and truncation errors.
A hybrid Yee/scalar-wave algorithm is introduced. The new method is designed to economically simulate the time-domain response of planar circuit geometries while generating results which are numerically identical to the Yee algorithm but at approximately one-half the computation time and two-thirds the memory.
Finally, the feasibility of using the hybrid Yee/scalar-wave algorithm method is demonstrated by computing the far-field radiation patterns of several tapered slot antennas (TSA). It is found that the E-plane results are in good agreement with measured results but that the H-plane results are greatly affected by the modeling of the antenna feed. (Abstract shortened by UMI.)
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