Hey Ernesto, I’ve used the approach outlined by Wolfgang and Daniel in my own work (multi physics problems, single DoFHandler with BC’s being transferred between a primary and secondary problem solved on subsets of the domain). Overall, it works really well so I’d back up their suggestion and recommend that you adopt it. Its mostly really just a question of finding common support points on the two surfaces, and seeing which DoF indices link up and transferring data from one solution vector to the other. I was looking though my code to see if I could share a snippet with you, but its so close in structure to the interpolate_boundary_values() (and still retains all of the original comments in the deal.II source :-) that its not really worth it.
Cheers, J-P > On 15 Jan 2020, at 07:48, Daniel Arndt <d.arndt.m...@gmail.com> wrote: > > Ernesto, > > Imposing strong boundary conditions should not be overly difficult in this > case. > Just as Wolgang said you should have a look at interpolate_boundary_values() > and replace the Function object evaluations on each cell by the function > values given through > a FEValues object initialized for your first solution. Assuming that you are > using interpolatory ansatz functions, this interpolation has to happen at the > support points of your target finite element. > In particular, these support points should be the quadrature points for the > FEValues object. > > Best, > Daniel > > Am Di., 14. Jan. 2020 um 01:50 Uhr schrieb Ernesto Ismail > <ernesto.ism...@gmail.com <mailto:ernesto.ism...@gmail.com>>: > Dear Prof. Bangerth, > > Thank you for your reply. > > I would ideally have liked to impose the boundary conditions strongly but it > looks like doing so will not be straight-forward. I will do some > investigations into applying the boundary conditions weakly and attempt that > first. > > One approach I had tried was to use Lobatto quadrature and use a quadrature > point history data structure to transfer the solution at the boundary. The > problem with this approach was that the differing element types lead to some > strange behaviours along the boundary. > > Thanks again, > Ernesto > > On Thursday, 9 January 2020 23:43:27 UTC+2, Wolfgang Bangerth wrote: > > Ernesto, > > > I am currently working with a staggered coupled system where I am solving > > several finite element problems in sequence. Up until now my boundary > > conditions have been fairly straightforward and I've been able to get > > meaningful results from my work. > > > > The finite element schemes I use for each step are fairly different, with > > some > > being discontinuous and of varying orders. > > > > I am now in a position where I need to use the solution of one of my steps > > as > > the boundary condition for the next (I actually need to combine two of them > > with a simple arithmetic function, but baby steps for now). I presume I > > need > > to use some sort of projection to achieve this, but I'm not exactly sure > > how > > to go about it. I thought to try and use the project_boundary_values() > > function to do what I need, but I am unsure how I would structure > > the boundary_functions argument. > > Do you need to enforce these boundary conditions strongly? If you can enforce > them weakly, then the solution of one problem only enters the weak form of > another problem (in that case through a boundary integral) and that is really > not very different from the way we do this in other problems where we have > multiple DoFHandlers -- e.g., in step-31. (Though my usual advice still holds > true that I think everything becomes simpler if you pack everything into one > DoFHandler). > > It gets more complicated if you want to impose strong boundary conditions. > You've already found the FEFieldFunction function, but it's complicated and > slow. A simpler way would be if you looked at the implementation of the > interpolate_boundary_values() function and identified where it is asking the > Function object for its values. That's the place where you'd need to somehow > combine your existing solutions into something else and turn that into a > constraint. > > Best > W. > > -- > ------------------------------------------------------------------------ > Wolfgang Bangerth email: bang...@colostate.edu <> > www: http://www.math.colostate.edu/~bangerth/ > <http://www.math.colostate.edu/~bangerth/> > > > -- > The deal.II project is located at http://www.dealii.org/ > <http://www.dealii.org/> > For mailing list/forum options, see > https://groups.google.com/d/forum/dealii?hl=en > <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 dealii+unsubscr...@googlegroups.com > <mailto:dealii+unsubscr...@googlegroups.com>. > To view this discussion on the web visit > https://groups.google.com/d/msgid/dealii/832bb83a-7e04-4243-9524-64db1bfc9345%40googlegroups.com > > <https://groups.google.com/d/msgid/dealii/832bb83a-7e04-4243-9524-64db1bfc9345%40googlegroups.com?utm_medium=email&utm_source=footer>. > > -- > The deal.II project is located at http://www.dealii.org/ > <http://www.dealii.org/> > For mailing list/forum options, see > https://groups.google.com/d/forum/dealii?hl=en > <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 dealii+unsubscr...@googlegroups.com > <mailto:dealii+unsubscr...@googlegroups.com>. > To view this discussion on the web visit > https://groups.google.com/d/msgid/dealii/CAOYDWbKY2%3D%2BBdWX4mh7guYEROFPT7mX8QR%3D4ED4KWymi_cD7Aw%40mail.gmail.com > > <https://groups.google.com/d/msgid/dealii/CAOYDWbKY2%3D%2BBdWX4mh7guYEROFPT7mX8QR%3D4ED4KWymi_cD7Aw%40mail.gmail.com?utm_medium=email&utm_source=footer>. -- 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. 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