Hi @Kun Cheng ,
To address your task of generating a list of all edges in a quadratic 3D mesh, I built upon the provided code and incorporate a method to differentiate between the vertices and mid-edge nodes in a tetrahedral element. In this context, each tetrahedral element consists of 10 nodes: 4 corner nodes, 6 edge midpoints, and 1 center node. Here is an updated MATLAB code snippet that generates the mesh and lists all edges correctly:
% Define the cubic dimensions
cubic = [100, 50, 20];
% Create a PDE model for thermal transient analysis
model = createpde(thermal="transient");
Note: createpde requires Partial Differential Equation Toolbox.
% Create geometry using multicuboid
geo = multicuboid(cubic(1), cubic(2), cubic(3), 'Zoffset', 0);
model.Geometry = geo;
For more information on multicubiod function, please refer to
https://www.mathworks.com/help/pde/ug/multicuboid.html?searchHighlight=multicuboid&s_tid=srchtitle_support_results_1_multicuboid
% Generate a quadratic mesh
model = generateMesh(model, GeometricOrder='quadratic');
For more information on generateMesh function, please refer to
https://www.mathworks.com/help/pde/ug/pde.pdemodel.generatemesh.html?searchHighlight=generateMesh&s_tid=srchtitle_support_results_1_generateMesh
% Visualize the generated mesh
pdemesh(model);
For more information on pdemesh function, please refer to
https://www.mathworks.com/help/pde/ug/femodel.pdemesh.html?s_tid=doc_ta
% Get mesh information
mesh = model.Mesh;
% Initialize an array to hold edges
edges = [];
% Extract edge data from the mesh
for i = 1:size(mesh.Elements, 2) % Loop through each element
% Get vertex indices for the current element (tetrahedron)
vertexIndices = mesh.Elements(:, i);
% Define edges for tetrahedron (6 unique edges)
elementEdges = [
vertexIndices(1), vertexIndices(2);
vertexIndices(1), vertexIndices(3);
vertexIndices(1), vertexIndices(4);
vertexIndices(2), vertexIndices(3);
vertexIndices(2), vertexIndices(4);
vertexIndices(3), vertexIndices(4)
]; % Append to edges array (removing duplicates)
edges = [edges; unique(elementEdges, 'rows')];
end% Remove duplicate edges (if any)
edges = unique(sort(edges, 2), 'rows');
% Display all unique edges
disp('Unique Edges in the Mesh:');
disp(edges);
As you can see above in the code snippet, the cubic geometry is created using multicuboid. The generateMesh function creates a quadratic mesh with specified geometric order. The Edge Extraction loops through each tetrahedral element in mesh.Elements, where each column represents an element.For each tetrahedron, define its six edges based on its four vertices, collect these edges into an array while ensuring uniqueness by sorting and removing duplicates.
Each edge is represented by its two endpoint node indices. Sorting ensures that (A, B) is treated the same as (B, A). The approach uses MATLAB's built-in functions like unique to streamline the process of eliminating duplicate edges.
This code should fulfill your requirement to generate and list all unique edges from a quadratic tetrahedral mesh while maintaining clarity and efficiency.
If you have further questions or need additional modifications, feel free to ask!
