On 8/27/19 2:23 PM, Charlie Z wrote:
>
> I find a conflict here is that::
> 1) TrilinosWrappers::PreconditionAMG can only be initialized with a
> matrix, but not a ApproximateSchurComplement;
> 2) step-20 uses ApproximateSchurComplement because we actually don't
> want to/can't assemble the Schur matrix or its inverse.
Yes, you correctly identified the issue. step-20 gets away with using
ApproximateSchurComplement as a preconditioner because, from the
perspective of GMRES, a preconditioner only has be able to provide a
matrix-vector product (i.e., apply itself to a vector).
But if you want to use an object to initialize a algebraic multigrid,
the AMG implementation needs to be able to do much more than just apply
the object to a vector -- it needs to build a multilevel hierarchy, and
for that it needs access to the elements that make up that matrix. The
problem is of course that ApproximateSchurComplement does not offer
access to the elements of the matrix it represents (because it never
explicitly computes them).
> Could you please give me a hint on how to solve this conflict in
> deal.II? Is it actually possible to assemble this B(DA^-1)BT directly?
Yes, of course. You can just multiply it out as the matrix-matrix
product of three matrices. The result is a square matrix of the right
size, with a rather large number of nonzero entries per row.
Best
W.
--
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Wolfgang Bangerth email: bange...@colostate.edu
www: http://www.math.colostate.edu/~bangerth/
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