How do I construct a mesh in PDE Solver from only the boundary points?

Basically, the title. I have a non-uniform or clustered mesh on which I would like to solve a particular PDE but I can't figure out how. I know the boundary points and nothing else. Any help?

Answer 1

[Vinayak]

Hi Ghazwan

You can use triangulation to get the connections and nodes, which could be fed into the ‘generateFromMesh’ function. I have a sample code with points in a distorted circle geometry, that are fed into ‘delaunayTriangulation’ and a mesh is generated post that.

% Generate random points 
numPoints = 10; 
theta = linspace(0, 1.95*pi, numPoints); 
r = 1; % Radius of the circle 
x = r * cos(theta) + rand(1, numPoints) * 0.1; % Adding small randomness 
y = r * sin(theta) + rand(1, numPoints) * 0.1; 

% Create a PDE model 
model = createpde(); 

% Generate Delaunay triangulation 
DT = delaunayTriangulation(x', y'); 

% Use the triangulation to define the geometry in the PDE model 
geometryFromMesh(model, DT.Points', DT.ConnectivityList'); 

% Generate the mesh 
mesh = generateMesh(model,'Hmax',0.2); % Adjust 'Hmax' as needed 

% Plot the mesh 
figure; 
pdemesh(model); 
axis equal; 

You can read more about “triangulation” and “geometryFromMesh” here:

https://www.mathworks.com/help/matlab/delaunay-triangulation.html

https://www.mathworks.com/help/pde/ug/pde.pdemodel.geometryfrommesh.html

I hope this helps!