Re: [Libmesh-users] Advice on splitting methods

[<an...@ma...>]

Thanks for the hint, this is exaclty what I was looking for. I'll let
you know!

Luca


On Fri, Mar 25, 2005 at 06:33:30AM -0600, Benjamin S. Kirk wrote:
> A fairly arbitrary sparsity pattern can be computed if you use the 
> DofMap::dof_coupling array.  By default, all DOFs are considered coupled 
> to each other, but it sounds like for your case (in 2D) you probably 
> want something like this:
> 
>  u v P
> |0 0 1|
> |0 0 1|
> |1 1 0|
> 
> to store L & L^T in the same matrix, or just the last row for L^T?
> 
> You should be able to modify the dof_coupling array, call 
> compute_sparsity, and build an appropriate matrix.
> 
> 
> Note that there are more options if you know you are working with PETSc 
> behind the scenes.
> 
> For example,  consider
> 
> PetscMatrix<> pmat = dynamic_cast<PetscMatrix<> >(mat);
> 
> pmat->get_mat();
> 
> allows you to access the PETSc Mat object directly.  You can then use 
> the PETScGetSubMatrix commands.
> 
> In fact, this might be the most straightforward thing to do.  You could 
> build a full matrix for a coupled system and then extract whatever 
> components you need.  You then might even be able to re-assemble the 
> full system if you want a fully coupled solver some time.
> 
> Anyway, these are my thoughts.  I know John has done some work on 
> special preconditioners for the Stokes system and has had to extract the 
> matrices you are interested in, so he could probably offer some more 
> suggestions.
> 
> You might need to add some code to make your job easier, if so I'll be 
> happy to help any way possible.
> 
> -Ben
> 
> 
> 
> la...@im... wrote:
> >Dear libmeshers, 
> > I've got an issue on how to organize my code.
> > For a start, I'm implementing a pressure correction solver for the
> >generalized Stokes problem. The code is now working great, the
> >solution is the right one, except that it could run way faster if it
> >didn't have to reassemble matrices and rhs's from scratch at each time
> >step. Since I'm planning to ultimately implement a semi-implicit
> >Navier-Stokes solver, I'll have to use a large number of time steps
> >and this issue is crucial.
> > The problem could be reassembled at each time step by storing the
> >single matrices (mass, diffusion) and adding them to form the system
> >matrix or multiplying them by a vector to form rhs terms. This would
> >solve performance issues, but there's a problem. Matrices in the Stokes 
> >system are M, the mass matrix, S, the diffusion (laplacian) matrix, and 
> >L the divergence matrix (whose transpose is the gradient matrix for the 
> >pressure). The problem resides in L: how can I store it? It's a
> >rectangular matrix, because it basically couples the velocity dofs
> >with the pressure dofs. Notice that I need it even in a 
> >pressure-correction scheme in order to assemble the rhs without looping 
> >over the elements
> >constructing the pressure gradients at hand.
> > Is there a way in which I can store the L matrix with the right
> >sparsity pattern, or is there an easy extension to limbesh I could
> >contribute? (Mind that this problem is potentially common to a lot of
> >splitting schemes)
> > I hope I've been clear enough, and thanks in advance for your help!
> >
> >Luca
> > 
> >
> 
> 
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-- 
Luca Antiga, PhD
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Biomedical Technologies Laboratory
Bioengineering Department, 
Mario Negri Institute
Villa Camozzi, 24020, Ranica (BG), Italy
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email: an...@ma...
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