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Georg Thomas Mandl 2026-01-14 18:42:17 +01:00
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Sheet_6/assembling.m Normal file
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% assembling of the stiffness matrix and the load vector for a given mesh
% in 1D
function [K,f_vec] = assembling(nodes,lambda,f)
n_nodes = length(nodes);
K = zeros(n_nodes);
f_vec = zeros(n_nodes,1);
h_diff_vec = nodes(2:end) - nodes(1:end-1); % step width
for k = 1:n_nodes-1
% stiffness matrix
lambda_int = integral(lambda, nodes(k), nodes(k+1));
K_loc = lambda_int/h_diff_vec(k)^2*[1,-1;-1,1];
K(k:k+1,k:k+1) = K(k:k+1,k:k+1) + K_loc;
% right hand side
phi_left = @(x) (nodes(k+1)-x)/h_diff_vec(k).*f(x);
phi_right = @(x) (x-nodes(k))/h_diff_vec(k).*f(x);
f_loc = [integral(phi_left,nodes(k),nodes(k+1)); integral(phi_right,nodes(k),nodes(k+1))];
f_vec(k:k+1) = f_vec(k:k+1) + f_loc;
end
end