Set Neumann Boundary Conditions to PDEModel

Hello, I want to solve the Laplace equation on a 2-D rectangular grid. I'm using the "applyBoundaryCondition" function to determine the boundaries.

On one side I have a constant Dirichlet boundary, applyBoundaryCondition(model,'Edge',3,'u',v);, and on the other two sides I have constant Neumann boundaries, applyBoundaryCondition(model,'Edge',[1,4],'q',0,'g',0);.

On the fourth side I want to use a Neumann boundary but instead of g=constant I have a vector that represents the value at each boundary point applyBoundaryCondition(model,'Edge',[1,4],'q',0,'g',[1:100]);. Is it possible to define 'g' as a vector like this and if not how can I do it?

Answer 1

[Alan Weiss]

The documentation describes how to set boundary conditions. There is a worked example here.

For your case, you probably need to interpolate the g value as a function of x or y in order that the boundary condition is defined everywhere. You can use interp1 or any other interpolation method you like.

Good luck,

Alan Weiss

MATLAB mathematical toolbox documentation

[d]

Thanks for the quick response, if I understand correctly I should do something like this?:

define a function like this:

 xj=1:100;
 j=xj.^2;
 myufun = @(region,state)interp1(xj,j,region.x);

and call the function like this:

 bc=applyBoundaryCondition(pdemod,'Edge',2,'q',0,'g',myufun,'Vectorized','on');

is it valid to do it like this?

[Alan Weiss]

That looks correct to me. (Of course, if you really had such a simple formula for your g values, you wouldn't use interp1, you would just give the formula.)

Alan Weiss

MATLAB mathematical toolbox documentation

[d]

Is there a way to implement this directly to the PDE Toolbox? I attached a screenshot to clarify. (unfortunately j is not that simple and I cant express it as simple function)

[Alan Weiss]

Oh, I didn't realize that you were using the PDE app. I don't think that the PDE app uses functions in this syntax. Instead, I think that it uses functions in a syntax described here.

IMHO, it is much easier to use command-line functions with a PDEModel object.

Alan Weiss

MATLAB mathematical toolbox documentation

[d]

I tried them both and in every one of them I had another problem. With the PDEmodel object I can write the function but the mesh using "generate Mesh" was not good. In contrasts, by using the PDE app I was able to create a good mesh but I can't write a function in the way I want. (The mesh problem is described the second question of mine: refine mesh in PDEModel )