I'm writing a similar code to Praveen, and had some additional questions,
having looked at the documentation for mesh_loop as well as step-47,
step-51, and the code gallery entry for the second-order LDG solver.
For a scheme that has a mixed-formulation element-local system (Q,U) as
does the LDG scheme in the code gallery, it is desirable to instead
eliminate the gradient Q on each cell and assemble a linear system only in
U. This amounts to a Schur complement taken on each cell--that is,
[[ A B ]] [Q] = [ 0 ]
[[ -B^T C ]] [U] [ F ]
and a cell contribution to the LHS of the global linear system KU = L,
where K = C + B^T A^{-1} B. My question is the following:
- It seems that since cell interior data (A inverse) is needed to
premultiply the B operator (which contains face terms), it makes more sense
to loop over each cell and handle the faces of the cell manually, like in
step-51, which performs a similar element-local static condensation.
- In the spirit of step-51, my idea is to use mesh_loop, but only use
the cell-assembly part and pass dummy functions to the face_worker and
boundary_worker arguments. Is that a sensible way to do it, or should I be
using a different MeshWorker function?
- Or alternatively, is there a way to use the face_worker function, but
preserve the data on the cell to the left and right? It seems expensive to
recompute the inverse mass matrix on every interface, for each adjacent
cell.
Best,
Corbin
On Tuesday, June 1, 2021 at 12:06:42 AM UTC-4 Wolfgang Bangerth wrote:
> On 5/31/21 9:36 PM, Praveen C wrote:
> >
> > It this how it should be used ?
> >
>
> Something like this. You might want to look at step-47 which assembles
> face
> terms for interior faces.
>
> Best
> W.
>
> --
> ------------------------------------------------------------------------
> Wolfgang Bangerth email: [email protected]
> www: http://www.math.colostate.edu/~bangerth/
>
>
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