Finite Difference Time Domain is a numerical method deployed for solution of Maxwell’s equations in a medium subject to boundary conditions. Propagation of electromagnetic fields in a medium can be mathematically analyzed by means of Maxwell’s equations. The solution of Maxwell’s equations yields the spatial variation and time history of propagating electric and magnetic fields. Since the Maxwell’s equations involve integrals and differentials, numerical approximation of the same is needed so that a computer can solve them.
Differentiation is approximated as first order backward or forward difference, thus, converting a differential equation in to a difference equation. This step applied to all the curl equations will yield a set of 6 difference equations.
We need to model the medium of propagation so as to characterize the wave nature of propagation of electric and magnetic fields. For this purpose, a one dimensional space is approximated as a set of points with a finite but close enough distance between them. A two dimensional space is divided into an array of square of rectangular grids and three dimensional space is divided into an array of cubes or cuboids. Such an approximation is constrained by stability conditions so that the solution converges.
The grid dimension should be a sub-multiple of wavelength of propagation. Incase more than one wavelength exists, the smallest of all is taken. In this project, we have taken the grid dimension to be one-twelfth of the wavelength. However, even smaller grids yield better results but such small grids will directly impact the computational time and memory requirements. Smaller grids imply more grids to approximate the medium which increases the memory space needed to store variables. Also smaller grids would increase the execution time as the number of space points at which calculations are to be carried out is increased.
In FDTD, the electric fields and magnetic fields are staggered in both... [continues]
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