%--------------------------
 % @Author: Jingqiao Hu
 % @Date: 2021-10-06 14:46:55
 % @LastEditTime: 2021-10-06 14:46:55
%--------------------------
%Heaviside function 
function H=Heaviside(phi,globalx,globaly,epsilon) 
    alpha=1e-3; % parameter alpha in the Heaviside function 

    num_all=[1:(globalx+1)*(globaly+1)]'; 
    num1=find(phi>epsilon); 
    H(num1)=1; 
    num2=find(phi<-epsilon); 
    H(num2)=alpha; 
    num3=setdiff(num_all,[num1;num2]); 
    H(num3)=3*(1-alpha)/4*(phi(num3)/epsilon-phi(num3).^3/(3*(epsilon)^3))+ (1+alpha)/2; 
end