Hello Praveen, that is exactly what I am after - having all but the first basis function have a zero integral. Will take a look at what you sent me, thank you.
Regards, Lukáš Korous On Fri, Apr 21, 2017 at 6:14 AM, Praveen C <[email protected]> wrote: > Hello Lukas > > You may want to look up this thread > > https://groups.google.com/d/msg/dealii/RbcPNELLHZA/eZxRYjzlVXIJ > > I started implementing Taylor basis as FE_DGT class some years back but > did not complete it, see code here > > https://bitbucket.org/cpraveen/deal_ii/src/master/fe_dgt/?at=master > https://bitbucket.org/cpraveen/deal_ii/src/master/dg/2d_ > scalar_unsteady_taylor/?at=master > > FE_DGT is basically monomials, see > https://bitbucket.org/cpraveen/deal_ii/src/497a4c7b2aa0d07f9 > 2e7c9f58a2b4c00ca1c1206/fe_dgt/fe_dgt.cc?at=master& > fileviewer=file-view-default#fe_dgt.cc-135 > > These shape functions are defined in physical space. They are not > orthogonal. > > In my implementation, I transform as > > (x-xc)/h, (y-yc)/h where h = cell diameter > > You probably want to transform as > > (x-xc)/dx, (y-yc)/dy > > then calculate shape_value, subtract integral of shape_function also. Then > all shape functions have zero integral and only first one has non-zero > integral. This should be possible to implement for Cartesian grids. > > > Best > praveen > > On Wed, Apr 19, 2017 at 1:50 AM, Lukas Korous <[email protected]> > wrote: > >> Hello, >> >> for solving the (ideal) MHD equations, I would like to implement two >> custom shapesets: >> >> >> - one for the flow part, completely discontinuous, scalar FE space, >> analogy to FE_DGQ, but based on Taylor expansion in the cell center >> >> >> - this should be the easy part, but I would like to ask how to go >> about it in deal.ii - I would like to implement at least linear and >> quadratic functions >> >> >> - one for the magnetic field, a vector Hdiv space, analogy to >> FE_RaviartThomas, but in this case a space of divergence-free functions >> that satisfy div F = 0 within the reference cell >> - this I assume will be more difficult, but here I am only after >> linear functions >> >> >> Reasoning behind usage of these is in https://github.com/l-korous/mh >> deal/blob/master/papers/Compumag2017_MHD.pdf, section IV.A (divergence >> free space), IV.B (Vertex-based limiting which needs the Taylor-basis FE >> space). Currently the code in https://github.com/l-korous/mh >> deal/blob/master/code/ is failing for DG order > 0 because of >> undershoots and overshoots present in the unlimited flow solution, mag >> field works, but there is no divergence cleaning employed. >> >> >> Could you please point me in the right direction where to start with this >> and what all needs to be done for these two new shapesets / spaces to be >> employed? >> >> >> Many thanks >> >> -- >> The deal.II project is located at http://www.dealii.org/ >> For mailing list/forum options, see https://groups.google.com/d/fo >> rum/dealii?hl=en >> --- >> You received this message because you are subscribed to the Google Groups >> "deal.II User Group" group. >> To unsubscribe from this group and stop receiving emails from it, send an >> email to [email protected]. >> For more options, visit https://groups.google.com/d/optout. >> > > -- > The deal.II project is located at http://www.dealii.org/ > For mailing list/forum options, see https://groups.google.com/d/ > forum/dealii?hl=en > --- > You received this message because you are subscribed to a topic in the > Google Groups "deal.II User Group" group. > To unsubscribe from this topic, visit https://groups.google.com/d/ > topic/dealii/NDiUu3qESOM/unsubscribe. > To unsubscribe from this group and all its topics, send an email to > [email protected]. > For more options, visit https://groups.google.com/d/optout. > -- The deal.II project is located at http://www.dealii.org/ For mailing list/forum options, see https://groups.google.com/d/forum/dealii?hl=en --- You received this message because you are subscribed to the Google Groups "deal.II User Group" group. To unsubscribe from this group and stop receiving emails from it, send an email to [email protected]. For more options, visit https://groups.google.com/d/optout.
