How to apply boundary conditions in pde toolbox without edge/face id?

I have a geometry which is changing slightly at each iteration and hence its boundary points change too. I want to apply a Neumann Condition to a "macroscopic edge"( which is a concatenation of several small edges) but I don't know their id from "Edgelabels" as they are more than 100 in number and change at every iteration.

How can I apply the Neumann's condition to the edge set {e_i1, e_i2,......,e_in}?

Answer 1

[Ravi Kumar]

If you have the same Neumann BC on all edges then you can try:

applyBoundaryCondition(model,'neumann','Edge',1:model.Geometry.NumEdges,'g',1)

Where g = 1 BC is used for illustration.

[Vishal Srivastava]

Okay. That seems good. But I have to apply that condition on only n out of n+7 edges in my geometry. Moreover, I am not sure that my those n edges would be indexed from 1:n or 2:n+1.or anything regular in model.Geometry.NumEdges.

Now I don't know what to do do next?

[Ravi Kumar]

I that case, how are the edges appearing? How are you creating the changed geometry in each iteration?

Any chance you get to know the IDs of the 7 edges that needs to have a different BC?

[Vishal Srivastava]

Okay. So I am attaching the geometry at two different instances. The lower boundary is composed of several (nearly 100) edges that get changed by delta_y and hence the change in geometry. I want to solve a pde in this dynamic domain(without the circle) and have a Neumann's condition on the lower changing boundary.

The IDs of rest 7 edges(4 of circle and other 3 of rectangle) is not remaining regular as I checked in two snaps (attached). Those 7 edges have IDs {103, 104, 105, 106, 51, 52, 53} and {103, 104, 105, 106, 54, 55, 56} at two instances when total edges were same in both cases. (=106).

On a broader scale, can you suggest some other possible way to solve pde with dynamic geometry(or some form of parametrization that may ease up the process)?

My goal is: 1)Initiate the simulation. 2)Solve pde with BC on lower(shape changing curvy boundary) 3)Evaluate the change in boundary delta_y = f(u, grad_u etc.) 4)Repeat

Answer 2

[Ravi Kumar]

Here is another approach to determine which edges are micro edges (the little ones at the bottom) and which edges are macro. This is rather a roundabout way, but it would work for you case.

I illustrate with a square example how to identify which edge is bottom edge without using its label, treat this as a micro edges of your case.

% Create a simple model, square geometry with four edges.
model = createpde;
geometryFromEdges(model,@squareg);

% Get hold on hadles to plot with edge labels on.
h1 = pdegplot(model,'EdgeLabels','on');
hp = h1.Parent;

edgeLabelsArray = hp.Children;

labelCells = {edgeLabelsArray(1:4).String};
labelNums = str2num(cell2mat(strip(labelCells','E')));

positionCells = {edgeLabelsArray(1:4).Position};
positionNums = cell2mat(positioncells');

% Y-Coordinate of labels.
yLocationOFLabels = positionNums(:,2);

% Tag an edge to be a macro edge if its label location is above a
% threshold.
yThreshold = -0.5;
macroEdgeFlag = yLocationOFLabels>yThreshold;

macroEdges = labelNums(macroEdgeFlag)
microEdges = labelNums(~macroEdgeFlag)

[Brandon Hayes]

This technique works well for geometry from the "geometryFromEdges" function. However, if you want to import an STL, I found it doesn't work exactly as is. It is close, but I found that there are hidden fields within the handle that must be accessed to get the data. Here is the modification I came up with to get things working. The key is that edgeLabelsArray(1) needs to refer to the "text' handle.

model_scaled = createpde(1);
g = importGeometry(model_scaled,fullfile(main_directory,[image_file(1:end-4),' -- solid.stl']));
scale(g,pixel_per_m_ratio);
mesh_scaled = generateMesh(model_scaled,'Hmax',100e-6 .* pixel_per_m_ratio);

figure
imshow(im_raw)
hold on
h = pdegplot(model_scaled,'EdgeLabels','on');
hold off

hp = h.Parent;
edgeLabelsArray = hp.Children;
edge_labels = edgeLabelsArray(1).String; %get the edge labels of the text field
edge_labels_vector = zeros(1,length(edge_labels));
for ii = 1:length(edge_labels)
    edge_labels_vector(ii) = str2num(strip(edge_labels{ii},'E'));
end
edge_vertex_data = edgeLabelsArray(1).VertexData; %get the vertex data where the label is placed

Answer 3

[Ronald Haynes]

Vishal - did you find a working solution to your problem? I have a very similar situation that I have not been able to find a robust solution for.