3D PDE modelling different c coefficients for different spatial regions

Hi,
I have a geometry imported into MATLAB shown in the picture below. 
For reference, the cube describes tissue bed and the cylindrical holes describe blood vessel with dirichlet pressure boundary conditions.
I am trying to specify c coefficients to change the properties in a spherical region within the cube, 
with the coefficient inside and outside this spherical region set to different scalar values.

I know you cannot specify subdomains in the same way as in the 2D pde modeller, but I tried to use an "if statement" to spatially set c coefficients without much luck.

function c = c_region_3D(location,state)

%% Input variables for region which we want to alter

% sphere 1

xc_old1=0.1875;

yc_old1=0.1875;

zc_old1= 0.125;

r_old=0.1;

a=1; % counter for all voxels within cube

for i=1:length(location.x)

for j=1:length(location.y)

for k=1:length(location.z)

if ((location.x(i)-xc_old1).^2 + (location.y(j)-yc_old1).^2 + (location.z(k)-zc_old1).^2<=(r_old).^2)==1

c(1,a) = 3.3929e-13;

a=a+1;

else

c(1,a) = 4.4762e-13;

a=a+1;

end

end

end

end

However, I only seem to be able to provide a c matrix with the length of one side of the cube - how do I therefore reference 3D points to specify the c coefficient in this region?

Thank you!

Answer 1

[Ravi Kumar]

Hi Barnaby,

If all you want is different values of c for points within sphere and outside sphere, then you can just do this:

function c = c_region_3D(location,state)
xc_old1=0.1875;
yc_old1=0.1875;
zc_old1= 0.125;
r_old=0.1;

c = zeros(size(location.x));

%find IDs of points in sphere or not and use it for logical indexing.
Index_of_PointsInSphere = (location.x-xc_old1).^2 + (location.y-yc_old1).^2 + (location.z-zc_old1).^2<=(r_old).^2;
Index_of_Points_NOT_InSphere = ~Index_of_PointsInSphere;

c(Index_of_PointsInSphere) = 3.3929e-13;
c(Index_of_Points_NOT_InSphere) = 4.4762e-13;

end

Regards,

Ravi

[Barnaby Graff]

Thank you so much!