Hi Colin, On 24/04/16 00:28, Colin Cotter wrote:
Hi Firedrakers,
I'm revisiting the solver approach in the vertical slice model, to try to incorporate it better into dcore. A vertical slice model is obtained from a 3D model, but you assume that all the fields are independent of y, whilst retaining a fully 3D velocity vector.
There are two ways to achieve this: 1) Build a mesh that is only one element wide and periodic in the y-direction. 2) Split the velocity space into a part which is tangential to the slice plane (u,w), and a part which is normal to the slice plane (v). In compatible FEM this means making a 2D H(div) space for the tangential part, and a scalar DG space for v.
So far we have been doing 2) in a way that requires rather specialised code that is different from what we use in 3D, which makes the code very bloated and hard to test.
First of all, is 1) possible in Firedrake? If not, how difficult would it be to make it possible? This would be my preferred solution.
So you would like a mesh, I'll draw quads: x---o | | | | y---p Where the vertical edges and the vertices are periodic (i.e. x and o are topologically the same and similarly y and p). I think you might be able to do this if you talk directly to the dmplex API. First you make the topological cells you want, then you build a coordinate section (a functionspace) on that DM and set up your coordinates appropriately. We'd then have to do a little bit of plumbing to make sure that your could tell firedrake that the coordinate field petsc provides is already discontinuous.
If 1) is out, then I'd like to improve our approach to 2) so that it is less intrusive in our code. I'd really like to make a sum of spaces so that we get a 3D vector with the in plane components coming from an H(div) space and the out-of-plane components coming from a DG space.
This would imply that different basis functions in your element pull back differently. That is Right Out at the moment. If you would *only* like to treat these parts of the space as (u, v, w) when solving you could do the following. Make a 3-variable mixed space: W = XZ * Y * P In your solver options do: 'pc_fieldsplit_0_fields': '0, 1', 'pc_fieldsplit_1_fields': '2', # normal fieldsplit options for 0 and 1 where 0 now refers to the # XZY space and 1 to the P space. You have to turn off nested matrices for this to work.
Then, I could call this whole thing my velocity space and e.g. solve mixed velocity pressure problems using it. Is *this* possible? If not, how difficult would it be to make it possible?
Basis functions with different pullback is difficult I think, and requires serious re-engineering all through the form compiler pipeline. The solver trick I just showed should "work right now". Cheers, Lawrence