# Simulation with Matlab: wave scattering

## Illustration of Radar cross section reduction via active treatment

First the animation: that is video from figure 4., introducing wave scattering and some stealthness principles, here the principle of surface treatment (for example with an absorbing medium) for radar signals reduction.

Simulation and computationnal aspects rely on finite difference method, see for example (french) this page and also for example (also french) introduction to Matlab programming, and more specifically activities 8, simulation of monodimensionnal wave scattering, 9, simulation of bidimensionnal wave scattering, and 10, simulation of wave scattering inside a medium.

About the simulation and animation on which result is shown on top, the Matlab code is:

```
clear all;close all
clc;
c=8;
Lx=100;Ly=Lx;
Nx=150;Ny=150;
dx=Lx/Nx;dy=Ly/Ny;
x=linspace(0,Lx,Nx);
y=linspace(0,Ly,Ny);
dt=sqrt(dx^2+dy^2)/(2*c);
nu=1; % Source frequency
Temis=4; % source emitting duration
T=20;
t=[0:dt:T];Nt=length(t);
gax=c^2*dt^2/dx^2;
gay=c^2*dt^2/dy^2;
% Source location
sx=round(Nx/8);
sy=round(Ny/8);
u=zeros(Nx,Ny,Nt);
%% Obstacle 1
Ox=round(Nx/2);Oy=round(Ny/2);% centre
for k=2:Nt-1
for i=2:Nx-1
for j=2:Ny-1
tmp1=u(i-1,j,k)+u(i+1,j,k)-2*u(i,j,k);
tmp2=u(i,j-1,k)+u(i,j+1,k)-2*u(i,j,k);
u(i,j,k+1)=2*u(i,j,k)-u(i,j,k-1)+gax*tmp1+gay*tmp2;
end
end
if (k*dt<Temis)
u(sx,sy,k+1)=2*sin(2*pi*nu*k*dt);
else
u(sx,sy,k+1)=0;
end
%
% Obstacle(s):
for l=0:10
X=Ox+l;
for XX=-5:5
Z=X+XX;
u(Z,-Z+2*X,k+1)=0;
u(Z+1,-Z+2*X,k+1)=0;
end
end
% Absorbing condition (CLA)
% on the front face
% (from source and radar point of vue)
% of the object
X=Ox;
for XX=-5:5
Z=X+XX;
u(Z,-Z+2*X,k+1)=u(Z-1,-Z+2*X-1,k);
end
for XX=-4:5
Z=X+XX;
u(Z,-Z+2*X+1,k+1)=u(Z-1,-Z+2*X,k);
end
%
% Not wnated reflections:
u(1,:,k+1)=u(2,:,k);
u(Nx,:,k+1)=u(Nx-1,:,k);
u(:,1,k+1)=u(:,2,k);
u(:,Ny,k+1)=u(:,Ny-1,k);
end
% For source drawing purpose
u(sx,sy,:)=10;
% For obstacle drawing purpose
for l=0:10
X=Ox+l;
for XX=-5:5
Z=X+XX;
u(Z,-Z+2*X,:)=1;
u(Z+1,-Z+2*X,:)=1;
end
end
X=Ox;
for XX=-5:5
Z=X+XX;
u(Z,-Z+2*X,:)=1.5;u(Z-1,-Z+2*X-1,:)=2;
end
for XX=-4:5
Z=X+XX;
u(Z,-Z+2*X+1,:)=1.5;u(Z-1,-Z+2*X,:)=2;
end
fig=figure(1);clf;whitebg('w')
colormap(jet)
MM=[];
for k=1:2:Nt
subplot(211);
%imagesc(squeeze(u(:,:,k)));
pcolor(squeeze(u(:,:,k)));
axis off,axis square
shading flat
caxis([-0.5 2])
%colorbar
subplot(212),hold on
set(pp,'linewidth',3')
pp=plot(t,zeros(size(t)),'--k');
set(pp,'linewidth',0.5')
axis([0 T -0.6 0.6])
xlabel('Temps [ms]','fontsize',16)
ylabel('Amplitude','fontsize',16)
grid on
%pause(0.01)
MM=[MM getframe(fig)];
end
%break
movie2avi(MM,'Anim.avi')
```

Video resulting from

`movie2avi`

is usually a heavy (if not
really huge) one.
One can directly enable Matlab to use some codecs, see

`movie2avi`

parameters, via
`help movie2avi`

or, also see Matlab alternative solution to video generation:
`VideoWriter`

,
which is to used nearly the same way as `movie2avi`

,
but is a rather more complete with respect to codecs;
see the list of available "profiles"
`VideoWriter.getProfiles()`

Another alternative is to convert video after Matlab process, via for example

`ffmpeg`

`ffmpeg -i film.avi film.mp4`

which one can then use directly use, for example, inside html5 <video> (as at the top of page), or to convert to animated gif, via

`convert`

utility
(`ImageMagic`

software)
`convert -loop 2 film.avi film.gif`