User-defined near null space

[fverdugo]

Hi! First, let me congratulate you for this package, I have been using it and it performs very well! It's faster than PETSc GAMG in many cases according to my experience.

I am wondering if it is possible to pass a user-defined near null space to the SA-AMG routines. This is important e.g. in linear elasticity and other vector-valued problems.

By looking at this line

AlgebraicMultigrid.jl/src/aggregation.jl

Line 18 in 1714fa4

B = ones(T,n)

it looks like the near null space is hardcoded to be a vector of ones. Thus, I guess that the answer to my question is NO at the moment.

I would like to know if somebody is working on this feature. If not, I can try to address it myself and file a PR.

[ranjanan]

Thank you for your kind words and for using the package!

Yes, I can have definitely have that be an optional argument with default as ones(T,n). Feel free to send a PR. It should be a quick change. I'll merge as soon as tests pass. Thank you!

[fverdugo]

Yes, I can have definitely have that be an optional argument with default as ones(T,n). Feel free to send a PR. It should be a quick change.

Perhaps this is not sufficient. In general, the near null space can have several vectors, so size(B,2) can be > 1. I don't know if the code will support the case when B is a matrix. I'll try once I have some time.

[learning-chip]

Came across the same issue. Note that pyamg.aggregation.smoothed_aggregation_solver allows near-nullspace candidates B of shape (N, K). As long as the SA setup logic follows PyAMG, passing a 2-D matrix B should be fine.

[termi-official]

Support for near null space handling of classical (Ruge-Stüben) AMG is still not supported, yet. A starter on the underlying theory can be found here https://doi.org/10.1002/nla.688 for someone interested in grabbing this.

[fverdugo]

Hi all,

For the record, we implemented the option of a user-defined near nullspace in the AMG solver in PartitionedArrays. It is implemented for both (sequential) SparseMatrixCSC and (parallel/distributed) PSparseMatrix objects. This means that it works also in large-scale parallel computations using MPI.

See here for more details:

PartitionedArrays/PartitionedArrays.jl#167