The slice operation is only for
graphical post-processing. You cannot use a sliced solution into
computations because the obtained vector represent the value of
the solution on a cut mesh representing the computed intersection.
The obtained vector is no longer a dof vector on the meshfem mfu.
The standard way to compute this error is to produce a cut
integration method, and just compute the L2 or H1 norms in a
standard way with it. You can produce cut integration method with
the MeshLevelSet and MeshIM('levelset') objects. An example of use
in the python test program "demo_fictitious_domains.py"
Le 18/12/2018 à 18:54, Yassine ZAIM a
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
gf.Slice(('comp',('ball', +1, [x0, y0], r)), m, 5)
sl.export_to_vtk('App_Solution.vtk', 'ascii', mfu,
sl.export_to_vtk('Exc_Solution.vtk', 'ascii', mfu,
sl.export_to_vtk('Error-Ex-App.vtk', 'ascii', mfu,
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
gf.compute(mfu, Uex, 'interpolate on', sl)
gf.compute(mfu, Uap, 'interpolate on', sl)
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)
I get the following error in the "compute"
function (of the errors) :
getfem('compute', mf, U, what, *args)
(Getfem::InterfaceError) -- The trailing
dimension of argument 2 (an array of size
4670) has 4670 elements, 289 were expected.
question is how to calculate the error just in
the interesting domain (physical domain, slice
sl in my case).
you in advance.
in Applied Mathematics
Yves Renard (address@hidden) tel : (33) 04.72.43.87.08
20, rue Albert Einstein
69621 Villeurbanne Cedex, FRANCE