Dear getfem++ users,
I am trying to learn how to implement the fictitious domain method for the
simple problem of Poisson. My domain of interest Omega is a circle of
center (*x0=0,y0=0*) and radius *r=0.35*. I made the resolution in the
fictitious domain (the square [-0.5, 0.5]^2) and after that, I used the
slice to restrict my solution to the physical domain.
sl = gf.Slice(('comp',('ball', +1, [x0, y0], r)), m, 5)
sl.export_to_vtk('App_Solution.vtk', 'ascii', mfu, Uap)
sl.export_to_vtk('Exc_Solution.vtk', 'ascii', mfu, Uex)
sl.export_to_vtk('Error-Ex-App.vtk', 'ascii', mfu, Uap-Uex)
When I see the approximate and the exact solution in addition to the error
I can say that I get a good approximate solution. But I am trying to get
the optimal order of convergence (h and h^2) like in the papers "J.
Haslinger and Y. Renard" or "E. Burman and P. Hansbo". So I interpolate the
exact and approximate solution in the slice (domain of interest).
Ue = gf.compute(mfu, Uex, 'interpolate on', sl)
U = gf.compute(mfu, Uap, 'interpolate on', sl)
And after that I tried to calculate the error for different values of
NX=[16,32,..]
L2error = gf.compute(mfu, U-Ue, 'L2 norm', mim)
H1error = gf.compute(mfu, U-Ue, 'H1 norm', mim)
such that :
mim = gf.MeshIm('levelset',mls,'inside', gf.Integ('IM_TRIANGLE(6)'))
and mfu.set_fem(gf.Fem('FEM_PK(2,1)'))
But I get the following error in the "compute" function (of the errors) :
return getfem('compute', mf, U, what, *args)
RuntimeError: (Getfem::InterfaceError) -- The trailing dimension of
argument 2 (an array of size 4670) has 4670 elements, 289 were expected.
My question is how to calculate the error just in the interesting domain
(physical domain, slice sl in my case).
Thank you in advance.
--
*ZAIM Yassine *
*PhD in Applied Mathematics*
