phi_gradient.m

hodge decomposition for 2D vector fields.

function gradphi=phi_gradient(triangle,mesh) 
%% generate the Basis Gradient Table 
%% triangle: the Grid Table 
%% mesh: the Node Table 
%% gradphi: the resulted Basis Gradient Table 
M=size(triangle,1); 
gradphi=zeros(M,3,2); 
area2=get_area2(triangle(1,:),mesh); %% calculate the 2*triangle_area 
AB=zeros(3,2); 
for i=1:M 
y0=mesh(triangle(i,1),1); 
x0=mesh(triangle(i,1),2); 
y1=mesh(triangle(i,2),1); 
x1=mesh(triangle(i,2),2); 
y2=mesh(triangle(i,3),1); 
x2=mesh(triangle(i,3),2); 
AB(1,1)=y1-y2; 
AB(1,2)=x2-x1; 
AB(2,1)=y2-y0; 
AB(2,2)=x0-x2; 
AB(3,1)=y0-y1; 
AB(3,2)=x1-x0; 
for j=1:3 
for k=1:2 
gradphi(i,j,k)=-AB(j,k);  
end; 
end; 
end; 
gradphi=gradphi/area2; 
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% 
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%