How to Specify Coefficients for parabolic equation in Function Form

Hi, I've been trying to calculate the 2-D voltage distribution using functional pdetool. (Two thin dielectrics with air gap between) I want to specify the epsilons for each material. air: ep=ep_0, dielectric: ep=ep_r.

Since the parabolic(u0,tlist,model,c,a,f,d) produces the solution to the FEM formulation of the scalar PDE problem d*u_t - (c*u_r)_r + a*u = f, the coefficient 'c' is key in this issue.

Here I attached my matlab code. In the code, I tried as follow:

c=@(p,t,phi,t0) cfunction(p,t,ep,ep_r,z_end,z_start); %c=1; %
a=0;
f=0;
d=1e-5;
tlist=0:period/100:period;
phi = parabolic(0, tlist, pdem, c, a, f, d);

function c=cfunction(p,t,ep,ep_r,z_end,z_start)%phi,time,
% ep= 8.854e-14; % Epsilon_0 changed in cm order
% ep_r = 8.0; % relative dielectric constant (Al2O3: 9.1, Quartz: 8, Acryl: 2.6, Teflon: 2)
% z_end=0.5; % gap distance in cm

it1=t(1,:);
it2=t(2,:);
it3=t(3,:);
ypts = (p(2,it1)+p(2,it2)+p(2,it3))/3;

n=length(ypts);
c=zeros(n,1);

for i=1:n
    if ypts(i) <= z_end && ypts(i) >= z_start
        c(:,i)=ep;
    else
        c(:,i)=ep*ep_r;
    end
end

But it didn't work! What should I do?

[Alan Weiss]

In what way didn't it work? What is the error or other result that you got?

Alan Weiss

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