1. A NEW ELEMENT-ORIENTED MODEL FOR COMPUTATIONAL ELECTROMAGNETICS
- Author
-
Hamid Magrez and Abdelhak Ziyyat
- Subjects
Physics::Computational Physics ,Computer science ,Numerical analysis ,Physics::Medical Physics ,Finite-difference time-domain method ,Physics::Optics ,Physics::Classical Physics ,Condensed Matter Physics ,Differential operator ,Electronic, Optical and Magnetic Materials ,Computational physics ,Power (physics) ,Electromagnetism ,Computational mechanics ,Computational electromagnetics ,Applied mathematics ,Electrical and Electronic Engineering ,Element (category theory) - Abstract
In this paper, we present a new model using a Fourdimensional (4D) Element-Oriented physical concepts based on a topological approach in electromagnetism. Its general finite formulation on dual staggered grids reveals a flexible Finite-Difference Time-Domain (FDTD) method with reasonable local approximating functions. This flexible FDTD method is developed without recourse to the traditional Taylor based forms of the individual differential operators. This new formulation generalizes both the standard FDTD (S-FDTD) and the nonstandard FDTD (NS-FDTD) methods. Moreover, it can be used to generate new numerical methods. As proof, we deduce a new nonstandard scheme more accurate than the S-FDTD and the known nonstandard NS-FDTD methods. Through some numerical examples, we validate this proposal, and we show the power and the advantage of this Element-Oriented Model.
- Published
- 2012