Integral on cut boundary

Hello everyone,

I have a cut boundary that I have created using level set function (I am using xfem extension of NGsolve). My domain is square and it has a circular cut boundary in it defined by x^2+y^2=0.5^2. After doing my calculations, I want to calculate flux over this circular cut boundary which means calculating a boundary integral. After my previous question I know how to calculate integrals on mesh boundaries but I do not know how to calculate on this cut boundary, I keep getting wrong results or zeros. Analogous to my previous question I tried,

n_ls = grad(level_set_p1)* (-1/grad(level_set_p1).Norm()) 
VH1= H1(mesh, order=2, dirichlet="wall|inlet|outlet")
    gradu00 = GridFunction(VH1)
    gradu01 = GridFunction(VH1)
    gradu10 = GridFunction(VH1)
    gradu11 = GridFunction(VH1)

    et = GridFunction(VH1)
    et.Set(CoefficientFunction(1.0), definedon=level_set_cut)

    flux_x = Integrate(levelset_domain = { "levelset" : level_set_p1, "domain_type" : IF},
                                       cf=et*(gradu00*n_ls[0] + gradu01*n_ls[1]), mesh=mesh, order = order)
    flux_y = Integrate(levelset_domain = { "levelset" : level_set_p1, "domain_type" : IF},
                                       cf=et*(gradu10*n_ls[0] + gradu11*n_ls[1]), mesh=mesh, order = order)
    print ("flux_x:", flux_x)

Hi noname!

Your snippet is not helping me to reproduce your problem. Could you please post a full example that is not working as planned?!