> > With Mesquite I believe one would essentially redefine a triangulation in > whatever format it wants (I think you provide nodal coordinate and > connectivities), tell it which nodes remain fixed (i.e. provide some > constraints) and then simply specify some algorithm with which it must > update the nodal coordinate positions. So you would effectively give it a > set of mapped coordinates of the triangulation and it returns a new set for > you. The difference between these new mapped points and the reference grid > nodal coordinates is your euler vector. > > Ignoring here are only three real complexities with this approach: > 1. ... > 2. Translating this Euler vector into something thats relevant to the > FESystem for your problem (*this is what you're struggling to > conceptualise, but its really not difficult at all*). > 3. ... > Yes, this is what I am struggling to understand, you have put it very simply. Along that direction
> I would create a auxiliary system of dim x linear FE_Q's, which have > support points that coincide with the vertices. Then the issue of relating > DoFs and vertex locations is trivial because of these > <https://www.dealii.org/developer/doxygen/deal.II/classDoFAccessor.html#a5560151b5407e4851d5c1009c7753764> > three > <https://www.dealii.org/developer/doxygen/deal.II/namespaceGridTools.html#addb822f0e3068e48640ecc981ee6c1e6> > functions > <https://www.dealii.org/developer/doxygen/deal.II/namespaceGridTools.html#a9b7e2ca8ecd26a472e5225ba91a58acb>, > > which are valid when using Q1 elements. > I can see how this is trivial for linear FE_Q's, and these three links should make this concrete. I think that one must disconnect the problem that you're solving and solve the mesh update problem as a completely separate problem; this ties in with what Wolfgang has also said below. This is advantageous because one can then reuse this algorithm for various multiphysics problems (e.g. fluid-structure interaction), or just to increase the mesh quality before starting a simulation! I think that one must disconnect the problem that you're solving and solve > the mesh update problem as a completely separate problem; this ties in with > what Wolfgang has also said below. This is advantageous because one can > then reuse this algorithm for various multiphysics problems (e.g. > fluid-structure interaction), or just to increase the mesh quality before > starting a simulation! > I do agree with this, which really makes this particular rabbit hole (Mesquite) very attractive. I would create a auxiliary system of dim x linear FE_Q's, which have > support points that coincide with the vertices. Then the issue of relating > DoFs and vertex locations is trivial because of these > <https://www.dealii.org/developer/doxygen/deal.II/classDoFAccessor.html#a5560151b5407e4851d5c1009c7753764> > > three > <https://www.dealii.org/developer/doxygen/deal.II/namespaceGridTools.html#addb822f0e3068e48640ecc981ee6c1e6> > > functions > <https://www.dealii.org/developer/doxygen/deal.II/namespaceGridTools.html#a9b7e2ca8ecd26a472e5225ba91a58acb>, > > which are valid when using Q1 elements. Once one's solved the mesh update > problem, one then populates the Euler solution (displacement) vector > corresponding to this auxiliary DoFHandler. Then you can just do an > interpolation / projection of this vector onto your current FE space, or > update the triangulation vertices if desired. This also eliminates any > issues that arise if, say, your primary problem solves some displacement > with quadratic or discontinuous elements. or if the displacement is only > one component of the global solution. > > My thinking is that one could add the following functionality to the > library: > 1. A function that takes in a triangulation and a (possibly empty) Euler > vector defining the initial mapped coordinates of the triangulation > vertices, and some boolean constraints vector. This would then return an > optimal Q1 Euler vector as computed by Mesquite. > 2. A function that actually > <https://www.dealii.org/developer/doxygen/deal.II/step_18.html#TopLevelmove_mesh> > > moves > <https://www.dealii.org/developer/doxygen/deal.II/step_42.html#PlasticityContactProblemmove_mesh> > > the triangulation vertices for you based on this vector. > 3. A function that would interpolate the optimal Q1 Euler vector onto a > given FE space, which would presumably represent the displacement solution > to some other problem. > > Does this make sense? > Yes, this makes sense. To be clear, the functionality in step 2*. A function that actually moves the triangulation vertices for you based on this vector*. is not strictly necessary in the present context, is that right? -- 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 dealii+unsubscr...@googlegroups.com. For more options, visit https://groups.google.com/d/optout.
