Program16 1D FDTD with Perfectly Matched Layer boundary condition

The Berenger PML condition is introduced in 1D FDTD

Youtube Links :-
http://www.youtube.com/watch?v=RE8_Yw_Nn8s
http://www.youtube.com/watch?v=e-aOe7CYjBo
http://www.youtube.com/watch?v=jwRZWX4cpIY
http://www.youtube.com/watch?v=mEQC2urDU-c

Written for Course :-
Computational Electromagnetics, Fall 2011
Department of Electrical Engineering
Indian Institute of Technology Madras (IITM)
Chennai - 600036, India

Authors :-
Sathya Swaroop Ganta, B.Tech., M.Tech. Electrical Engg.
Kayatri, M.S. Engineering Design
Pankaj, M.S. Electrical Engg.
Sumantra Chaudhuri, M.S. Electrical Engg.
Projesh Basu, M.S. Electrical Engg.
Nikhil Kumar CS, M.S. Electrical Engg.

Instructor :-
Dr. Ananth Krishnan
Assistant Professor
Department of Electrical Engineering
Indian Institute of Technology Madras
http://www.ee.iitm.ac.in/~ananthk

Description :-
The 1D TEM wave is x-directed z-polarized TEM wave containing the y-directed magnetic field Hy and z-directed electric field Ez. The time update in Yee Algorithm is done using Leapfrog time-stepping. Here, the H fields are updated every half time-step and E fileds are updated every full time-step. This is shown by two alternating vector updates spanning entire spatial grid inside a main for-loop for time update spanning the entire time-grid. Yes, there are No For Loops except for time steps. The vector updates span only a part of spatial grid where the wave, starting from source, has reached at that particular time instant (exploiting sparse vectors) avoiding field updates at all points in the grid which is unnecessary at that time instant. The spatial and temporal parameters are not unit less and are given real values. Mostly parameters of free space are used except that very less electrical and magnetic conductivities of 4 x 10^4 units are incorporated. The boundary condition here is Perfectly Matched Layer (PML) boundary condition where the fields near the boundary are attenuated over a predetermined length of boundary width before they reach the boudary to a zero value at the boundary using a polynomially increasing electrical conductivity value over the boundary width with maximum at the boundary and also chosing a magnetic conductivity value at every point in the boundary width to avoid reflection at that point.