Apply Dirichlet BC on Vertex

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For solvability my problem needs to have at least a single boundary node set as Dirichlet. From the image attached, I would like to place u=0 at vertex 1. I have tried (and it worked) to use a miniscule edge near that vertex and place Diriclet conditions on it. What I don't like about that approach is that since it was more than a single node involved in the tiny edge, I was concerned that it could impact the results.
The two edges (edge 1 and 4) adjacent to vertex 1 should have a homogeneous Neumann condition (u'=0).
Is there a way to use a function and logic (example below) to have the code use Neumann on edges 1 & 4 but when x=xmax and y=ymin if uses Dirichlet?
Somewhat like this:
myPhantomFuncArgs= @(location,state) myPhantomFunc_Q(location,state,xmax,ymin);
applyBoundaryCondition(model,"neumann","Edge",[EdgeBotNotAnode EdgeRightWall],"q",myPhantomFuncArgs,"g",0);
function funcQ = myPhantomFunc_Q(location,state,xmax,ymin)
if (location.x < xmax || location.y > ymin) % Defines NOT vertex 1
funcQ = 0;
else
funcQ = 1; % Condition when at vertex 1.
end
end
This does not work since when funcQ is 1, there is still the gradient portion of the Neumann BC expression!
Thanks for any input.
Paul

采纳的回答

Torsten
Torsten 2025-4-16
Is there a way to use a function and logic (example below) to have the code use Neumann on edges 1 & 4 but when x=xmax and y=ymin if uses Dirichlet?
No. Boundary conditions have to be set on objects one dimension lower than the region where the PDEs are defined. Since you work in 2d, these boundary objects must be 1d, thus edges.
  6 个评论
Paul Safier
Paul Safier 2025-4-16
And that's fine, but it would allow me to insure that just a single node is set as Dirichlet. When I used the tiny edge method, I wasn't sure how to get just a single node in that little edge. Do you know how to push for that?
Torsten
Torsten 2025-4-17
I have no experience with the PDE Toolbox in particular, but usually, gridding praeprocessors allow to mesh the edges first and then to use this boundary mesh as starting point to measure the interior of the domain. Maybe the User Guide or Support can answer if and how this can be done.

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