Hi Jie,
thanks a lot. The link to your repository was very helpful. I could
significantly reduce the number of iterations using your implementation
of computing the pressure laplacian through:
K_p = B diag(velocity_mass_matrix)^-1 B^T.
I have tested the dependence of the preconditioner on the time step and
the mesh size and observed that it is likely to be mesh independent,
i.e. if the mesh is refined the number of outer (GMRES) iterations does
not change, which is great.
However there is a dependence on the size of the time step. Both
variants with assembly and your implementation show an increase in the
number of iterations.
time step
iterations with B B^T
iterations with assembly
1e-5
6 to 7
6 or 16 ringing
1e-4
8 to 9
18 to 19
1e-3
10 to 11
21 to 22
1e-2
12 to 14
24 to 27
1e-1
23 to 24
51 to 54
Did you make the same or similar observations? I have read some of the
literature and as far as I understand it the preconditioner should be
independent of the step size and viscosity.
Another point I would like to raise is related to mesh independence,
which is not quite true. In every step the solution of the pressure
laplace matrix (K_p) requires by far the largest number of iterations. I
am monitoring the iterations of all subsolvers:
7 GMRES iterations for stokes system, (A: 8, Kp: 682, Mp: 60)
For A (velocity block) one cycle of TrilinosWrappers::PreconditionAMG is
used. Mp is preconditioned using PreconditionSSOR and for Kp I am using
SparseILU. For the example quoted the pressure space has 4800 dofs. I am
wondering why the SparseILU with roughly 100 iterations per precondition
step does such a bad job in this case.
Of course, I don't expect you to answer all of this but it would great
if you make some comments about your experience with this
preconditioner. By the way I am also using an IMEX scheme in my solver,
see https://github.com/sebglane/BoussinesqFluidSolver/tree/modular_version .
Best wishes,
Sebastian
On 01.11.18 17:30, Jie Cheng wrote:
Hi Sebastian,
I think what you described is correct. I could not see why it did not
work out. But I recommend reading Timo's dissertation. Also, for the
implementation, you can check out my code for the implicit scheme
<https://github.com/OpenIFEM/OpenIFEM/blob/master/source/insim.cpp#L56>
and explicit-implicit scheme
<https://github.com/OpenIFEM/OpenIFEM/blob/master/source/insimex.cpp#L42>.
Best,
Jie
On Thu, Nov 1, 2018 at 5:58 PM SebG <seb_gl...@gmx.de
<mailto:seb_gl...@gmx.de>> wrote:
Dear Jie, dear deai.ii user,
I am working on the Cahouet-Chabbard preconditioner in context
buoyancy-driven flow problems. Somehow my preconditioner does not
work quite well. The number of iterations depends on the time
step, which should not be the case. With more than 50 iterations
it is also quite large. I would like to ask if you or someone else
could provide some details of your implementation or give tips.
The velocity block of the system matrix is given by:
alpha / timestep * M + gamma * c * K .
M, K are the velocity mass and stiffness matrix. The scalars alpha
and gamma are related to the time discretization and c is a
dimensionless parameter. If I am not wrong, the Cahouet-Chabbard
Schur complement approximation is given by
S^-1 = alpha / timestep * K_p^-1 + gamma * c * M_p^-1 .
I am assembling the pressure stiffness and pressure mass matrix
explicitly. However my problem is a pure Dirichlet problem w.r.t.
the velocity, which in contrast mean that preconditioner is using
Neumann BCs. Therefore, I am constraining one pressure dof, which
regularizes the pressure laplace matrix. This approach is
discussed in another thread
<https://groups.google.com/forum/#!msg/dealii/HBQD_WXuNOs/w0A56WAf2WcJ>.
For this reason I have two ConstraintMatrix object one for the
system matrix and one for the preconditioner.
I also attached my code which is based step-32 but in serial.
Best wishes,
Sebastian
Am Freitag, 20. Oktober 2017 09:36:07 UTC-7 schrieb Jie Cheng:
Hi Martin and Wolfgang
Thank you very much for the helpful comments and references.
I'll start to read the works you mentioned.
Jie -- I think this would be a very interesting program
for others as well.
Would you be interested in contributing it to the code
gallery?
I'd love to contribute after I work it out!
Jie
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