2D FDTD of a region with Perfectly Matched Layer boundary

2D FDTD of a region with Perfectly Matched Layer (PML) boundary condition

Youtube links:-
http://www.youtube.com/watch?v=hTNY26TBETY&feature=related
http://www.youtube.com/watch?v=tZ1rlO48xMM&feature=related
http://www.youtube.com/watch?v=CVecY3wHehE&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 not normalized to 1 but are given real and known values. The update is done using standard update equations obtained from the difference form of Maxwell's curl equations with very low electric and magnetic conductivities of 4x10^(-4) units incorporated in them. 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 here, the space-step length is taken as 1 micron instead of 1 unit in unitless domain assumed in previous programs. 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. Also, here, the matrices used as multiplication factors for update equations are initialized before the loop starts to avoid repeated calculation of the same in every loop iteration, a minor attempt at optimization.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 choosing a magnetic conductivity value at every point in the boundary width to avoid reflection at that point. Also, here, Berenger's PML condition is used where in the field Ez is split into two components Ezx and Ezy and the components are attenuated using separate electric and magnetic conductivities in the two directions (sigmax and sigma_starx in x direction and sigmay and sigma_stary in the y direction).