@parallel function diffusion3D_step!(T2, T, Ci, lam, dt, dx, dy, dz)
    @inn(T2) = @inn(T) + dt*(lam*@inn(Ci)*(@d2_xi(T)/dx^2 + @d2_yi(T)/dy^2 + @d2_zi(T)/dz^2));
    return
end

function diffusion3D()
# Physics
lam        = 1.0;                                        # Thermal conductivity
cp_min     = 1.0;                                        # Minimal heat capacity
lx, ly, lz = 10.0, 10.0, 10.0;                           # Length of computational domain in dimension x, y and z

# Numerics
nx, ny, nz = 8, 8, 8;                              # Number of gridpoints in dimensions x, y and z
nt         = 3;                                          # Number of time steps
dx         = lx/(nx-1);                                  # Space step in x-dimension
dy         = ly/(ny-1);                                  # Space step in y-dimension
dz         = lz/(nz-1);                                  # Space step in z-dimension

# Array initializations
T   = @zeros(nx, ny, nz);
T2  = @zeros(nx, ny, nz);
Ci  = @zeros(nx, ny, nz);

# Initial conditions (heat capacity and temperature with two Gaussian anomalies each)
Ci .= 1.0./( cp_min .+ Data.Array([5*exp(-(((ix-1)*dx-lx/1.5))^2-(((iy-1)*dy-ly/2))^2-(((iz-1)*dz-lz/1.5))^2) +
                                   5*exp(-(((ix-1)*dx-lx/3.0))^2-(((iy-1)*dy-ly/2))^2-(((iz-1)*dz-lz/1.5))^2) for ix=1:size(T,1), iy=1:size(T,2), iz=1:size(T,3)]) )
T  .= Data.Array([100*exp(-(((ix-1)*dx-lx/2)/2)^2-(((iy-1)*dy-ly/2)/2)^2-(((iz-1)*dz-lz/3.0)/2)^2) +
                   50*exp(-(((ix-1)*dx-lx/2)/2)^2-(((iy-1)*dy-ly/2)/2)^2-(((iz-1)*dz-lz/1.5)/2)^2) for ix=1:size(T,1), iy=1:size(T,2), iz=1:size(T,3)])
T2 .= T;                                                 # Assign also T2 to get correct boundary conditions.

# Time loop
dt = min(dx^2,dy^2,dz^2)*cp_min/lam/8.1;                 # Time step for the 3D Heat diffusion
for it = 1:nt
    @parallel diffusion3D_step!(T2, T, Ci, lam, dt, dx, dy, dz);
    T, T2 = T2, T;
end

return true
end
