## PDE toolbox: Undefined function 'mtimes' for input arguments of type 'function_handle'.

Asked by Flo brd

### Flo brd (view profile)

on 2 Oct 2018
Latest activity Commented on by Flo brd

### Flo brd (view profile)

on 3 Oct 2018
Hi everyone,
I have a bit of a hard time finding a way to use the output of my function handle:
effStress = @(~,state) (2700*9.81*4000*1e-6)-state.u;
K = 1e-12-(0.04343*((0.012+0.013)/2));
Dcore=(K*effStress);
I understand that I apparently cannot multiply K with effStress, but even a matrix multiplication doesnt work.
Could anyone help me on that?
Cheers, Flo

Dennis

### Dennis (view profile)

on 2 Oct 2018
You probably need to provide an input to effStress. Small example:
eff=@(a) a+1; %eff is a function handle
%A=3*eff; %this does not work
A=3*eff(3) %this does.
Flo brd

### Flo brd (view profile)

on 2 Oct 2018
I did try something similar. It didn't work. My issue is that I am working with the PDE toolbox. I am trying to apply a non-constant variable (with the C coefficient if that helps)

### Tags ### Stephen Cobeldick (view profile)

Answer by Stephen Cobeldick

### Stephen Cobeldick (view profile)

on 2 Oct 2018
Edited by Stephen Cobeldick

### Stephen Cobeldick (view profile)

on 2 Oct 2018

A function handle is not a numeric array, it cannot be multiplied. You could either
1. evaluate the function to get a numeric value, and multiply that value:
>> S.u = 4;
>> effStress = @(~,state) (2700*9.81*4000*1e-6)-state.u;
>> K = 1e-12-(0.04343*((0.012+0.013)/2));
>> K*effStress(0,S) % evaluate effStress to get an output.
ans = -0.055345
2. define a new function that calls your function:
>> fun = @(s)K*effStress(0,s); % does not evaluate effStress.
>> fun(S)
ans = -0.055345

Ravi Kumar

### Ravi Kumar (view profile)

on 2 Oct 2018
Can you provide the context of usage with a complete example?? Which function of PDE Toolbox are you referring to? Is your question, what is the value of state.u that solver passes when solve a model?
Flo brd

### Flo brd (view profile)

on 3 Oct 2018
Sorry for the lack of data I was able to provide in the first place. So as said earlier, I am working with the PDE toolbox. I am trying solve for the equation of fick, and that works well I guess. Now I need to update a non-constant variable as the PDE solver solves the partial differential equation.
Here is the code we are interested in
N=1;
model = createpde(N);
%define boxes et generate mesh
height = 10;
length = 30;
r1 = [3 4 0 10 10 0 0 0 height height];
r2 = [3 4 10 20 20 10 0 0 height height];
r3 = [3 4 20 length length 20 0 0 height height];
gdm = [r1; r2;r3]';
g = decsg(gdm,'R1+R2+R3',['R1'; 'R2'; 'R3']');
geometryFromEdges(model,g);
msh =generateMesh(model,'Hmax',2);
nodes = msh.Nodes;
%set id to nodes
nodes(3,:)= linspace(1,size(nodes,2),size(nodes,2));
% BC
applyBoundaryCondition(model,'dirichlet','edge',[7,8,9,4,5,6],'h',0);
applyBoundaryCondition(model,'dirichlet','edge',[3,10,1,2],'h',1);
%specify coefficients for the equation described in the PDE
a =0;
f = 0;
d = 1;
Dcore= @(location, state) Diffusivity(location, state, 1e-16,6000, 2700, 200);
specifyCoefficients(model,'m',0,'d',d,'c',Dcore,'a',a,'f',f, 'face',1);
Followed by the Diffusivity function:
function Dh = Diffusivity(location,state,ki,depth,density,T)
N = 1; % Number of equations
nr = length(location.x); % Number of columns
Eff = zeros(N,nr); % Allocate to avoid size issue
confiningStress = density*9.81*depth;
effStress= (confiningStress*1e-6) - state.u;
tmp = effStress .*Eff;
Cp = 0.000000001;
T = T+273.15;
A=2.414*10^-5;
B=247.8;
C=140;
%temperature dependent viscosity
u = A*10^(B/(T-C));
%pressure dependent k
gamma = 0.1;
K=ki-(0.2*gamma.*tmp);
Dh = K./(u*Cp);
end
that compiles, but I am really unsure I've understood the way the c coefficient works https://uk.mathworks.com/help/pde/ug/c-coefficient-for-systems-for-specifycoefficients.html#bu5xabm-1
In my understanding, state.u represents the state of the equation u at a certain point of the solving process. As my function depends on a value u, I am trying to get that value through state.u to update Dcore accordingly.
Am I right in my understanding of function handle?
I've tried using those threads as a base reflection:
Cheers, Flo
Flo brd

### Flo brd (view profile)

on 3 Oct 2018
I changed a bit my function, following what I've understood from the matlab help (and I am pretty my understanding is wrong), and my error changed to a warning. it doesn't compile but maybe you help me on that one too. here is my function:
function Dh = Diffusivity(location,state,ki, depth,density, T)
N = 1; % Number of equations
nr = numel(location.x); % Number of columns
Dh = zeros(N,nr); % Allocate to avoid size issue
% Eff(1,:) = ones(1,nr);
confiningStress = density*9.81*depth*1e-6;
matConf = zeros(1,nr);
matConf(1,:)=confiningStress;
Cp = 0.000000001;
T = T+273.15;
A=2.414*10^-5;
B=247.8;
C=140;
%temperature dependent viscosity
u = A*10^(B/(T-C));
%pressure dependent k
gamma =0.1
Dh(1,:)=(ki-(0.2*gamma.*(matConf(1,:) - state.u(1,:))))./(u*Cp);
end
the error is now
Warning: Failure at t=1.132789e-12. Unable to meet integration tolerances without reducing the step size below the smallest value allowed (3.231174e-27) at time t.
I am completely lost.
Flo