Non-analytical Matrix-Free coefficient

[Thomas Cheetham]

Hello everyone,

I am currently developing a matrix-free code which has a non-analytical spatially varying coefficient. As in step-37 I am using a  Table<2, VectorizedArray<number>> to store evaluations of the  coefficient at all the quadrature points for a given cell batch.

I read my coefficient in from a CSV file corresponding to the values at DOF in a structured mesh which I am using to generate a FEFieldFunction object which i call for all quadrature points to initialize the values in the matrix-free coefficient table. This approach is fairly slow but works okay for the finest level (where the parallel distributed triangulation is the same as the structured mesh). However for coarser multigrid levels I run into issues where the cell within which I am trying to evaluate points is no longer owned by the current processor.

I was wondering if anyone has any suggestions as to how to get around this, or perhaps has any ideas for a faster approach?

Many thanks,

Tom 

[Timo Heister]

Hi Tom,

What we do in ASPECT is the following:
1. evaluate the coefficient on the active cells and store in a Table
(for each Q point)
2. Project into a FE_DGQ(k) on each cell and store in a finite element
coefficient vector (you can pick k, k=0 would be a constant per cell)
3. interpolate_to_mg() to get a coefficient vector on each multigrid level
4. convert to a Table (interpolate to quadrature points or store a
constant per cell)

You can see this in action here:
https://github.com/geodynamics/aspect/blob/0a1784a421d555240c7710b77fe157aea12bb66c/source/simulator/solver/stokes_matrix_free_local_smoothing.cc#L371

We do this because coefficient data is not available on coarser levels
and because, even if it was, it is unlikely to improve the convergence
to have the real coefficient on the coarser levels.

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[Thomas Cheetham]

Thank you for your help Timo, that worked well.

Best wishes,

Tom