Problem with coefficient c in function form in solving 2D-PDE (PDE toolbox)

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Chiara Moreschini 2020-5-1

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评论： Chiara Moreschini 2020-5-1

I'm trying to solve a 2D-PDE with a c coefficent in function form, but i'm having some trouble in using location struct.

here is my function for c coefficient:

______________________________________________

function cmatrix = ccoeffunction(location,~)

n1 = 4;

nr = numel(location.x);

Ds=1.4e-10;

jv=2e-5;

cmatrix = zeros(n1,nr);

cmatrix(1,:) = Ds*ones(1,nr);

cmatrix(2,:) = jv*(location.y)+jv*((location.y).^3)/3;

cmatrix(3,:) = -jv*(location.x)+Ds*((location.x)./(location.y));

cmatrix(4,:) = Ds*ones(1,nr);

end

_______________________________________________

However the location struct passed to the function contains in fields x and y just one zero, so my function doesen't work correctly.

______________________________________________

location =

struct with fields:

x: 0

y: 0

z: 0

subdomain: 1

_______________________________________________

How can i pass to my function the correct location struct???

Thanks

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Answer 1

Ravi Kumar 2020-5-1

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Hi Chiara,

Solver will call the function several times to check if it is returing the correct format of coeff and so on, for these probing calls a single point is used. If you continue and get past this initial calls, you will be able to see that solver eventually calls with location of several Gauss points where element matrices are integrated.

Regards,

Ravi

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Chiara Moreschini 2020-5-1

Of course, thank you

This is the main program:

__________________________________________

cs0_b=0.2;

Bs=1e-3;

Ds=1.4e-10;

model_sangue = createpde();

rect=[3;4;0;300;300;0;0;0;100;100];

gd=[rect];

ns = char('rect1');

sf='rect1';

dl=decsg(gd);

pdegplot(dl,'EdgeLabels','on','FaceLabels','on')

xlim([0,300])

axis equal;

geometryFromEdges(model_sangue,dl);

pdegplot(model_sangue,'EdgeLabels','on')

applyBoundaryCondition(model_sangue,'dirichlet','Edge',4,'u',cs0_b);

specifyCoefficients(model_sangue,'m',0,'d',1,'c',@ccoeffunction,'a',0,'f',Bs);

setInitialConditions(model_sangue,cs0_b);

generateMesh(model_sangue);

tlist=0:100;

results_sangue = solvepde(model_sangue,tlist);

% PDE 2D plot

cs_b_nodi=results_sangue.NodalSolution;

pdeplot(model_sangue,'XYData',cs_b_nodi,'ZData',cs_b_nodi,'Mesh','on')

xlabel('z')

ylabel('r')

% evaluation of the solution in some random nodes

figure (2);

plot(tlist,cs_b_nodi(450,:), 'b');

xlabel('time');

ylabel('concentrazione in un nodo')

hold on

plot(tlist,cs_b_nodi(2,:), 'y');

hold on

plot(tlist,cs_b_nodi(900,:), 'm');

legend('nodo 450','nodo 2','nodo 900')

__________________________________________

This is the function for c coefficient:

__________________________________________

function cmatrix = ccoeffunction(location,~)

n1 = 4;

nr = numel(location.x);

Ds=1.4e-10;

jv=2e-5;

cmatrix = zeros(n1,nr);

cmatrix(1,:) = Ds*ones(1,nr);

cmatrix(2,:) = jv*(location.y)+jv*((location.y).^3)/3;

cmatrix(3,:) = -jv*(location.x)+Ds*((location.x)./(location.y));

cmatrix(4,:) = Ds*ones(1,nr);

end

__________________________________________

As you can see from the plot of the solution in some random nodes vs time the solution is the same everywere and does not change even if I change the costant jv in the function.

Thank you for your time

Chiara

Ravi Kumar 2020-5-1

Well, this could be it! You say your model in nm, I am thining you geometry then shoulod be 300 nm x100 nm. In which case you need to update your geometry creation to account the correct units:

rect=[3;4;0;[300;300;0;0;0;100;100]*1E-9];

If you do so, and plot the last time step solution, then this is what I get:

pdeplot(model_sangue,'XYData',cs_b_nodi(:,end),'ZData',cs_b_nodi(:,end),'Mesh','on')

Based on time-variation, I also think your tlist needs to scaled appropriately.

Regards,

Ravi

Chiara Moreschini 2020-5-1

Thank you very much!!

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Problem with coefficient c in function form in solving 2D-PDE (PDE toolbox)

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