2D FDTD in a unitless space with open boundary with matrix update instead of for loops

Youtube links:-
http://www.youtube.com/watch?v=cQguLD1of3s
http://www.youtube.com/watch?v=rIOeDMgUGsU&feature=related
http://www.youtube.com/watch?v=GndlMMsiG5Q&feature=related

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 :-

A 2D TM wave containing the xy-plane polarized magnetic field having components Hy and Hx and z-polarized electric field Ez. The fields are updated at every time step, in a space, where all physical parameters of free space are normalized to 1. The update is done using standard update equations obtained from the difference form of Maxwell's curl equations. The field points are defined in a grid described by Yee's algorithm. The H fields are defined at every half coordinate of spacesteps. More precisely, the Hx part is defined at every half y-coordinate and full x-coordinate and the Hy part is defined at every half x-coordinate and full y-coordinate and E fields i.e the Ez part is defined at every full x and full y-coordinate points. Also, the time update is done using Leapfrog time-stepping. Here, H-fields i.e Hx and Hy are updated every half time-step and E fields i.e Ez are updated every full time-step. This is shown by two alternating vector updates spanning only a part of spatial grid where the wave, starting from source, has reached at that particular time instant avoiding field updates at all points in the grid which is unnecessary at that time instant. These spatial updates are inside the main for-loop for time update, spanning the entire time grid.