construct_s1.m

hodge decomposition for 2D vector fields.

function S1=construct_S1(mv_x,mv_y) 
%% mv_x: horizontal coordinates of the grids 
%% mv_y: vertical coordinates of the grids 
%% S1: the element matrix S1 
%% generate the Node Table 
mesh=mesh_points(mv_x,mv_y); 
%% generate the Grid Table 
triangle=triangle_definition(mv_x,mv_y);  

%% generate the Basis Gradient Table 
gradphi=phi_gradient(triangle,mesh); 
M=size(mesh,1); 
S1=zeros(M,M); 
%% calculate the element matrix S1 
for i=1:M 
%% search for the neighboring triangles and neighboring nodes of a reference node 
    [neighbor_triangle neighbor_point]=get_neighbor(i,triangle); 
    L=length(neighbor_triangle); 
    for k=1:L 
        t=neighbor_triangle(k); 
        tri=triangle(t,:); 
        order_in_triangle=find(tri==i); 
        del_phi01=gradphi(t,order_in_triangle,1); 
        del_phi02=gradphi(t,order_in_triangle,2); 
        for j=1:3 
            mm=tri(j); 
            del_phi11=gradphi(t,j,1); 
            del_phi12=gradphi(t,j,2); 
            S1(i,mm)=S1(i,mm)+del_phi01*del_phi11+del_phi02*del_phi12; 
        end; 
    end; 
end; 
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