Hi hakim,
As per my understanding, you are facing issues while creating the matrices for elements and edges. To generate the p (nodes), t (elements), and e (edges) matrices for a rectangular mesh in MATLAB you can go through the following steps:
1. Define the node matrix (p):
% Define the node matrix
p = [x_nodes.'; y_nodes.'];
2. Generate the elements matrix(t):
Each grid cell is divided into two triangles using its four corner nodes, forming triangles (n1, n2, n3) and (n2, n3, n4). The matrix t has 5 rows: three for node indices, one placeholder, and one for the zone number.
% Fill the element matrix t
index = 1;
for i = 1:Nx-1
for j = 1:Ny-1
n1 = (j-1)*Nx + i;
n2 = n1 + 1;
n3 = n1 + Nx;
n4 = n3 + 1;
% Define two triangles for each rectangle
t(:, index) = [n1; n2; n3; 0; 1];
index = index + 1;
t(:, index) = [n2; n3; n4; 0; 1];
index = index + 1;
end
end
3. Generate the edge matrix(e) :
Each triangle's three edges in t are identified, sorted, and checked against a “map” to avoid duplicates. Unique edges are added to e with node indices, zone numbers, and subdomain assumptions. e is trimmed to represent unique edges accurately.
edge_index = 1;
edge_map = containers.Map('KeyType', 'char’, 'ValueType', 'any');
for i = 1:size(t, 2)
tri = t(1:3, i);
zone = t(5, i);
edges = [tri(1), tri(2); tri(2), tri(3); tri(3), tri(1)];
for j = 1:3
edge = sort(edges(j, :));
edge_key = sprintf('%d-%d', edge(1), edge(2));
if ~isKey(edge_map, edge_key)
e(1:2, edge_index) = edge;
e(5, edge_index) = zone
e(6, edge_index) = 0; % For exterior
e(7, edge_index) = zone; % For interior
edge_map(edge_key) = edge_index;
edge_index = edge_index + 1;
end
end
end
For more information on the “matrices” and “map” related functions in MATLAB, kindly go through the following documentations:
- Matrices: https://www.mathworks.com/help/matlab/math/creating-and-concatenating-matrices.html
- Map: https://www.mathworks.com/help/matlab/ref/containers.map.html
Hope it helps!
