Task 4

Project/ApplyRobinBC_mult.m

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+function [K, F] = ApplyRobinBC_mult(model, K, F, alpha, u_out)
+% ApplyRobinBC_mult
+% Implements Robin BC:
+%   lambda * du/dn + alpha*u = alpha*u_out
+%
+% alpha   : heat transfer coefficient
+% u_out   : outside temperature
+
+mesh = model.Mesh;
+nodes = mesh.Nodes;
+elements = mesh.Elements;
+
+% --- Find boundary edges ---
+edgesAll = [elements([1 2],:), elements([2 3],:), elements([3 1],:)];
+edgesSorted = sort(edgesAll,1);
+[edgesUnique,~,ic] = unique(edgesSorted','rows');
+counts = accumarray(ic,1);
+boundaryEdges = edgesUnique(counts==1,:);   % Nx2 array
+
+% --- Loop over Robin boundary edges ---
+for k = 1:size(boundaryEdges,1)
+    i = boundaryEdges(k,1);
+    j = boundaryEdges(k,2);
+
+    ri = nodes(1,i);
+    rj = nodes(1,j);
+    
+    if ri == 0 && rj == 0
+    % Edge lies on symmetry axis r = 0
+    % -> homogeneous Neumann BC, no Robin contribution
+        continue;
+    end
+
+    xi = nodes(:,i);
+    xj = nodes(:,j);
+
+    L = norm(xi - xj);   % edge length
+
+    % Robin boundary element matrices
+    Ke = alpha * L / 6 * [2 1; 1 2];
+    Fe = alpha * u_out * L / 2 * [1; 1];
+
+    % Assemble
+    K([i j],[i j]) = K([i j],[i j]) + Ke;
+    F([i j])       = F([i j]) + Fe;
+end
+end