Finite difference time domain FDTD -- MATLAB

Development of the technique “advection” equation

Calculate the spatial distribution at the next increment in time Setup a mesh in time and in space. The mesh in position extends beyond the points of interest. Initial conditions @ t = 0 time Calculate the spatial distribution at the next increment in time @ t = 1 position

Invoke periodic boundary conditions

Foreword difference in time Central difference in space

Finite difference Time domain “fdtd”

This is valid only for the interior range 2  n  N – 1

Periodic boundary conditions

Time  #1 -3L/8 -1/2 #2 -1L/8 1 ½ #3 +1L/8 3/2 #4 +3L/8

Example of the FDTD using the above procedure Initial conditions Time  2 3 4 -3L/8 -1/2 ½ 5/2 z -1L/8 1 -3/2 +1L/8 3/2 +3L/8

Lax to the rescue!

Periodic boundary conditions

 #1 -3L/8 #2 -1L/8 1 #3 +1L/8 #4 +3L/8

Example of the FDTD using the Lax procedure. Initial conditions Time  2 3 4 -3L/8 1 z -1L/8 +1L/8 +3L/8

First iteration & 50th iteration

Movie to illustrate the calculation

Frasson

Lewandowski