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

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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}?

Accepted Answer

Ravi Kumar
Ravi Kumar on 27 Feb 2018
Edited: Ravi Kumar on 27 Feb 2018
If you have the same Neumann BC on all edges then you can try:
Where g = 1 BC is used for illustration.
Vishal Srivastava
Vishal Srivastava on 27 Feb 2018
Edited: Vishal Srivastava on 28 Feb 2018
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

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More Answers (2)

Ravi Kumar
Ravi Kumar on 1 Mar 2018
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;
% 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)
  1 Comment
Brandon Hayes
Brandon Hayes on 27 Jan 2021
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']));
mesh_scaled = generateMesh(model_scaled,'Hmax',100e-6 .* pixel_per_m_ratio);
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'));
edge_vertex_data = edgeLabelsArray(1).VertexData; %get the vertex data where the label is placed

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Ronald Haynes
Ronald Haynes on 21 Nov 2018
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.

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