flexible block matrix

[Barry Smith]

   I concur with Satish, AIJ with inodes is essentially variable block  
size
so trying to force BAIJ when it is not appropriate is unnecessary.

   Barry

On Apr 21, 2008, at 9:53 AM, Jed Brown wrote:

> I am solving a Stokes problem with nonlinear slip boundary  
> conditions.  I don't
> think I can take advantage of block structure since the normal  
> component of
> velocity has a Dirichlet constraint and this must be built into the  
> velocity
> space in order to preserve conditioning.  An alternative formulation  
> involves a
> Lagrange multiplier for the constraint, but even with clever  
> preconditioning,
> this system is still more expensive to solve according to [1].
>
> In solving the (velocity-pressure) saddle point problem, many  
> approximate solves
> with the velocity system is needed in the preconditioner, hence I  
> need a strong
> preconditioner for the velocity system.  Currently, I am using  
> algebraic
> multigrid on a low-order discretization which works fairly well.   
> Since Hypre
> and ML only take AIJ matrices, perhaps I shouldn't worry about  
> blocking after
> all.  Is there a way to use MATBAIJ when some nodes have fewer  
> degrees of
> freedom?  Should I bother?
>
> Note that my method (currently just a single element) uses a high  
> order
> discretization on some elements and low order on others.  The global  
> matrix for
> the low order elements is assembled, but it is applied locally for  
> the high order
> elements taking advantage of the tensor product basis.  For the  
> preconditioner,
> a low order discretization on the nodes of the high order elements  
> is globally
> assembled and added to the global matrix from the low-order elements.
> Experiments with a single element (spectral rather than spectral/hp  
> element)
> show this to be effective, converging in a constant number of  
> iterations
> independent of polynomial order when using a V-cycle of AMG as a  
> preconditioner.
>
> Thanks.
>
> Jed
>
>
> [1] Bänsch, Höhn 2000, `Numerical treatment of the Navier-Stokes  
> equations with
> slip boundary conditions', SIAM J. Sci. Comput.
>