In [11]:

    

using Plots;
gadfly();


    

In [12]:

    

include("../fdtd/update.jl");
include("../fdtd/sources.jl");
include("../fdtd/boundaries.jl");
using update;
using sources;


    

    




WARNING: replacing module globals
WARNING: replacing module update
WARNING: replacing module globals
WARNING: replacing module sources
WARNING: replacing module boundaries

In [33]:

    

#Global parameters
size = 200;
endTime = 400;
num_snaps = 200;
snap_step = div(endTime, num_snaps);

eps1 = 4;
eps0 = 1;

#Grid

# Magnetic
hy = zeros(size);
mu = ones(size);

chyh = ones(size);
chye = ones(size);


# Electric
ez = zeros(size);
eps = ones(size);

cezh = ones(size);
ceze = ones(size);


for i in 1:99
    eps[i] = eps0;
end
for i in 100:size
    eps[i] = eps1;
end

#
# Left boundary ABC
#
boundaries.setup_first_order_abc!(eps, mu, 1, false)

#
# Right boundary CPML
#

# constants
dx = 1.0;
R0 = 1e-5;
m = 2.85;
# m = 4;
pml_width = 30.0;

# coeffs
sigma_max = -(m+1)*log(R0)/2/globals.imp0/(pml_width*dx)
sigma_x = zeros(size);
sigma_m_x = zeros(size);

for i in 1:int(pml_width)
    sigma_x[size-(i-1)] = sigma_max * real(Complex(((pml_width-i-0.5)/pml_width))^m)  
    sigma_m_x[size-(i-1)] = sigma_max * real(Complex(((pml_width-i)/pml_width))^m)
end

aex = exp(-sigma_x .* globals.imp0)-1
bex = exp(-sigma_x .* globals.imp0)

ahx = exp(-sigma_m_x .* globals.imp0)-1
bhx = exp(-sigma_m_x .* globals.imp0)

# arrays
p_hy = zeros(size);
p_ez = zeros(size);

# output params
ez_snapshot = Array{Any}(num_snaps);
hy_snapshot = Array{Any}(num_snaps);

refl = 0.0;
reflection_counter = zeros(num_snaps);
refl_counter_pos = 20;

trans = 0.0;
transmission_counter = zeros(num_snaps);
trans_counter_pos = 160;


    

In [34]:

    

# Time steps

for time in 1:endTime
    # Incident
    # ez_inc, hy_inc = sources.gaussian_source(50, time);
    delay = 30.
    width = 100.
    
    ez_inc = exp(-(time + 0.5 - (-0.5) - delay) * (time + 0.5 - (-0.5) - delay) / width);
    hy_inc = exp(-(time - delay) * (time - delay) / width);
    
    #
    # CPML
    #
    for i in 1:size-1
        p_hy[i] = bhx[i]*p_hy[i] + ahx[i]*(ez[i+1] - ez[i])
    end
    for i in 2:size
        p_ez[i] = bex[i]*p_ez[i] + aex[i]*(hy[i] - hy[i-1])
    end
    
    #
    # Magnetic
    #
        
    # Interior update
    for i = 1:size-1
        hy[i] = chyh[i] * hy[i] + chye[i] * (ez[i+1] - ez[i]) / globals.imp0 / mu[i]
    end
    
    # TFSF
    hy[49] -= hy_inc / globals.imp0 / mu[49]
    
    # CPML
    for i in 1:size-1
        hy[i] += p_hy[i]/globals.imp0/mu[i]
    end

    #
    # Electric
    #
       
    # Interior update
    for i = 2:size
        ez[i] = ceze[i] * ez[i] + cezh[i] * (hy[i] - hy[i-1]) * globals.imp0 / eps[i]
    end
    
    # TFSF
    ez[50] += ez_inc / eps[50]
 
    # ABC Left
    boundaries.first_order_diff_abc!(ez, 1, false)
    
    # CPML Right
    for i in 2:size
        ez[i] += p_ez[i]*globals.imp0/eps[i]
    end   
 
    refl += (ez[refl_counter_pos])^2;
    trans +=(ez[trans_counter_pos])^2;
    
    # Snapshots for animation
    if mod(time, snap_step) == 0
        t = div(time,snap_step)
        ez_snapshot[t] = (time, copy(ez))
        hy_snapshot[t] = (time, copy(hy).*globals.imp0)        

        # Counters
            reflection_counter[t] = refl;
            transmission_counter[t] = trans;
    end    
    
end


    

In [35]:

    

anim = Animation()

for i = 1:num_snaps
    p = plot(1:size, ez_snapshot[i][2], lab="Ez")
    plot!(1:size, hy_snapshot[i][2], lab="Hy*imp0")
    
    time = ez_snapshot[i][1]
    plot!(ann=[(150, 1.5, "time =$time")])
    plot!(ann=[(0, 1.1, "Mur ABC")])
    
    plot!(ann=[(80, 1.2, "Eps = $eps0")])
    plot!(ann=[(100, 1.1, "Eps = $eps1")])    
    plot!([100, 100], [-2, 2])
    
    plot!(ann=[(180, 1.1, "CPML")])
    
    R = reflection_counter[i]
    plot!(ann=[(refl_counter_pos, -1.1, "R = $R")])
    plot!([refl_counter_pos, refl_counter_pos], [-1, 1])
    
    T = transmission_counter[i]
    plot!(ann=[(trans_counter_pos, -1.1, "T = $T")])    
    plot!([trans_counter_pos, trans_counter_pos], [-1, 1])
    
    plot!(xlims=(1, 200), ylims=(-2, 2))
    frame(anim, p)
end
gif(anim, "./10_reflection.gif", fps=15)


    

    




INFO: Saved animation to /media/storage/Documents/Github/1d-fdtd/examples/10_reflection.gif






    
Out[35]:

In [36]:

    

R = reflection_counter[end] / (transmission_counter[end] + reflection_counter[end])
T = transmission_counter[end] / (transmission_counter[end] + reflection_counter[end])

print("T = $T\n")
print("R = $R\n")


    

    




T = 0.7987934988592996
R = 0.20120650114070035

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