THE NUMERICAL OF CHARACTERISTICS FOR ELECTROMAGNETICS

Abstract

The objective of this study is to explore the benefits of using the theory of characteristics to develop accurate and efficient numerical algorithms for Computational Electromagnetics. The present work adapts the numerical method of Characterisitics (MOC) from Computational Fluid Dynamics to the one-dimensional Maxwell curl equations in the time domain. The relevant theory of characterisitics is developed and the inverse matching method is used to develop two numerical algorithms based on different interpolation schemes in the initial data surface. Stability and dispersion for these algorithms are discussed. Results are given for one-dimensional model problems involving free space pulse propagation, scattering from perfect conductors and reflection/transmission for lossy dielectric materials. The model problems are designed to provide quantitative insight to both accuracy and efficiency for different classes of realistic application problems. The Finite-Difference Time-Domain (FDTD) method is used as a convenient reference algorithm for comparison. It is demonstrated that these algorithms have accuracy comparable to FDTD, but do not require staggered grid storage, which simplifies impedance boundary conditions and implementation on nonuniform grids. The thoery of characteristics demonstrates a very natural outer boundary condition without nonreflecting approximations or matched layers. A dispersion enhanced version of the MOC is also developed which has phase errors 50-5000 times lower than FDTD. This approach appears promising for development of dispersion enhanced characteristic based schemes for two and three dimensional applications.