[petsc-users] How to improve this solver for Navier-Stokes equation (based on fieldsplit and lsc)

[Thomas Witkowski]

Am 14.06.2012 15:06, schrieb Matthew Knepley:
> On Thu, Jun 14, 2012 at 9:01 PM, Thomas Witkowski 
> <thomas.witkowski at tu-dresden.de 
> <mailto:thomas.witkowski at tu-dresden.de>> wrote:
>
>     I try to implement an efficient solver for my FEM based unsteady
>     Navier Stokes code. The scenario I consider is realy simple: 2D
>     FEM with Taylor-Hood element, equi-spaced grid, simple channel
>     flow with prescribed inflow boundaries for the velocity, no
>     boundary conditions for the pressure. Because I want to
>
>
> With no pressure BC, you need to specify the null space. Look at SNES 
> ex62.
As so often, I forgotten about this :) As I have free outflow boundary 
for the velocity (so no Dirichlet boundary), I think, the nullspace must 
be somehow different than just setting a constant on all pressure nodes. 
So I want back to the even more simple case, the driven cavity scenario. 
Here I have dirichlet BC on all velocity components and boundaries and 
no pressure BC. There is no influence on the solver, whether I set the 
null space or not (I checked for it with -ksp_view that there is a null 
space set). Only when going from fgmres to gmres for the outer solver, 
setting the null space has some (positive) change in the solver 
convergence.

>     solve unsteady flows, at each timepoint an Ossen problem is solved
>     (implicit Euler time discretization, "trivial" linearization). For
>     using PETSc, I created a fieldsplit preconditioner, that is
>     configured in the following way:
>
>     mpirun -np 2 ./navier_stokes init/channel_parallel.dat.2d \
>     -ksp_type fgmres \
>     -pc_type fieldsplit \
>     -pc_fieldsplit_type SCHUR \
>     -pc_fieldsplit_schur_fact_type FULL \
>     -ksp_converged_reason \
>     -ksp_monitor_true_residual \
>     -fieldsplit_velocity_ksp_type preonly \
>     -fieldsplit_velocity_pc_type lu \
>     -fieldsplit_velocity_pc_factor_mat_solver_package mumps \
>     -fieldsplit_pressure_ksp_type gmres \
>     -fieldsplit_pressure_ksp_max_it 10 \
>     -fieldsplit_pressure_ksp_rtol 1.0e-2 \
>     -fieldsplit_pressure_pc_type lsc \
>
>
> This makes no sense unless you specify an auxiliary operator. Just 
> leave it at jacobi. When you use LU
> for velocity, it will converge in 1 iterate. Since it doesn't, it 
> means you have a problem with the null space.
So even for the driven cavity, the null space is set, and again I use 
the same solver, it needs something like 10 or 15 iterations. I don't 
understand your argument, that using LU for the velocity part, this 
solver should converge in 1 iterations. It still has an inexact solver 
for the Schur complement and the solver for the composite matrix in LSC 
is also inexact.

Thomas

>
>    Matt
>
>     -fieldsplit_pressure_lsc_ksp_type bcgs \
>     -fieldsplit_pressure_lsc_ksp_max_it 10 \
>     -fieldsplit_pressure_lsc_ksp_rtol 1.0e-2 \
>     -fieldsplit_pressure_lsc_pc_type hypre
>
>     The direct solver for the velocity part is just for debugging and
>     should be replaced when everything else works fine. The point is,
>     that I found this constellation to be not very efficient. It takes
>     around 20 to 30 iterations, which takes around 30 seconds on a
>     very small problem size (around 20000 global unknows for each
>     velocity component and 5000 global unknowns for the pressure) on a
>     very fast desktop CPU (some new Intel Xeno with 4 core). Any hints
>     for improvements?
>
>     Thomas
>
>
>
>
> -- 
> What most experimenters take for granted before they begin their 
> experiments is infinitely more interesting than any results to which 
> their experiments lead.
> -- Norbert Wiener

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