[Libmesh-users] Advice on splitting methods

[<la...@im...>]

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
 

-- 
Luca Antiga, PhD
----------------------------------------------
Biomedical Technologies Laboratory
Bioengineering Department, 
Mario Negri Institute
Villa Camozzi, 24020, Ranica (BG), Italy
----------------------------------------------
phone: +39 035 4535-381
email: an...@ma...
web:   http://villacamozzi.marionegri.it/~luca
----------------------------------------------