# Want to use barbellgraph.mat as a mesh

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##### 1 Comment

Walter Roberson
on 19 Feb 2024

### Accepted Answer

Malay Agarwal
on 19 Feb 2024

Edited: Malay Agarwal
on 20 Feb 2024

Hi Michelle,

I understand that you want to use the data in “barbellgraph.mat” file, used in the example “Partition Graph with Laplacian Matrix”, as a 2D mesh to solve PDEs on.

Please try the following code:

% Load the MAT file

load barbellgraph.mat

% Create a graph using A

G = graph(A, "omitselfloops");

% Extract the endpoints of each edge as two separate variables

x = G.Edges.EndNodes(:, 1);

y = G.Edges.EndNodes(:, 2);

% Create a triangulation

tri = delaunayTriangulation(x, y);

% Create a geometry using the triangulation

geom = fegeometry(tri);

% Create a model using the geometry

% Note: Change AnalysisType according to use case

model = femodel("AnalysisType","structuralStatic","Geometry", geom);

The code above:

- Loads the “.mat” file and creates a graph “G” using the variable “A”.
- Extracts the endpoints for each edge in the graph as two separate variables “x” and “y”. For example, if the graph has edges (a, b) and (c, d), “x” is “[a c]” and “y” is “[b d]”.
- Creates a Delaunay triangulation “tri” using the endpoints of the edges of the graph.
- Uses the triangulation to create a geometry “geom”.
- Creates a model “model” using the geometry, which can now be used to solve PDEs. Please note that you might have to change “AnalysisType” in the call to “femodel” depending on your use case.

The triangulation and the geometry can be plotted as a sanity check using the following code:

triplot(tri);

pdegplot(geom, FaceAlpha=0.3);

The resultant mesh looks as follows:

pdemesh(model);

You can refer to the following resources for more details:

- "graph" documentation: https://www.mathworks.com/help/matlab/ref/graph.html.
- "delaunayTriangulation" documentation: https://www.mathworks.com/help/matlab/ref/delaunay.html.
- "fegeometry" documentation: https://www.mathworks.com/help/pde/ug/fegeometry.html.
- "femodel" documentation: https://www.mathworks.com/help/pde/ug/femodel.html.

Hope this helps!

##### 5 Comments

Malay Agarwal
on 23 Feb 2024

Edited: Malay Agarwal
on 23 Feb 2024

Hi Michelle,

The reason why the number of nodes decreases is due to the call to "generateMesh" with the "GeomtericOrder" name-value argument. The name-value arguments of "generateMesh" are used to modify the mesh generation, as specified in the documentation: https://www.mathworks.com/help/pde/ug/pde.pdemodel.generatemesh.html?s_tid=doc_ta#bupct6k-3:~:text=example-,___,%2CName%2CValue),-modifies%20the%20mesh.

If the model is plotted after these lines:

% Stores the P and T variables

load pt.mat

model = createpde;

geometryFromMesh(model,P',T');

specifyCoefficients(model,"m",0,"d",1,"c",1,"a",0,"f",0);

applyBoundaryCondition(model,'dirichlet','Edge',[1,2,3,4],'u',0);

It has the expected mesh:

pdeplot(model);

I don't think the "generateMesh" call is required here since the model's geometry was created using variables "P" and "T", and the expected mesh is already part of the model. You should be able to solve PDEs after the call to "applyBoundaryCondition".

This can also be confirmed by looking at the "Mesh" property of "model" before and after calling "generateMesh":

- Before the call to "generateMesh":

model.Mesh

- After the call to "generateMesh":

generateMesh(model, "GeometricOrder", "linear");

model.Mesh

Hope this helps!

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