[Dune-devel] smoother aggregation preconditioner using DUNE

[Bao Kai]

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Hi,

Currently, we are trying to make a smoother aggregation two-level
method (maybe multiple level later). The basic formulation is:

x: fine degree of freedom
x_c : coarse degree of freedom
A = fine-matrix
P = prolongation-operator
Ac = P^T A P : coarse matrix
move to fine is: P*x_c
move to coarse P^T*x
Given that the structure of P is defined with sufficient nonzero elements
P=(I -(1/lambda)* A)^n P_I
where P_I is the the representation of your prolongation operator.

The basic task is to be able to generate and operate on to parallel
index sets. One for the coarse grid and one for the fine grid (and
then more if multilevel is considered),  and the connection between
them is given by P. This is a rather general task.

Do you know if it exist some utilities for this in dune and where to
search for it? For me it seems like dune-fem which operate on function
spaces or any of the modules gluing grids should use similar things.

In addition basic tasks is parallel sparse matrix matrix
multiplication where the structures can be generated ones and where
the index sets of the two "vector spaces" is used is need. Has anyone
made general implementations of this in DUNE?

And also, as far as I understand correctly, the redistributeMatrix
only deals with square matrices. For us, the P is rectangular, is
there anything has been done related to redistribute rectangular
matrices. We guess there the remoteIndices for both direction will be
needed.

Thanks.

Regards,
Kai