On Wed, Jan 15, 2014 at 5:15 PM, Benjamin Hepp <benjamin.h...@bsse.ethz.ch> wrote: > Hello, > > my question from a few days ago might have been a bit imprecise. I > reformulate it and hope this helps: > > I could not find any details in the FiPy documentation so I assume it is > using first order Lagrange elements psi_i, where i is the element index.
I guess that is correct. FiPy just uses linear interpolation between cell centers. > I would like to compute the integrals > <psi_i, psi_j> > and > <grad psi_i, grad psi_j> > for each i, j. Is this possible with FiPy? This is confusing. In the FVM, $\psi_i$ only really means anything in cell $i$. By definition, \psi_i = \int \psi dV_i / \int dV_i over a given cell. The integrals might not make sense in the context of the FVM, while making sense in terms of the FEM. This may be to do with the notion of local support in FEM, where the $phi_i$ is defined on the whole domain, but is only non-zero in the neighbourhood of element $i$ so the integral makes sense. If one was to do this naively with the output from fipy, then you would just have a diagonal matrix, which doesn't show you anything. What you need is a reconstruction of the non-averaged discretized $\psi$'s. I don't believe that FiPy has any inbuilt functionality to do this. Hope that helps or at least clarifies things a bit. -- Daniel Wheeler _______________________________________________ fipy mailing list fipy@nist.gov http://www.ctcms.nist.gov/fipy [ NIST internal ONLY: https://email.nist.gov/mailman/listinfo/fipy ]
