[petsc-users] How to speed up geometric multigrid

[Mark F. Adams]

On Sep 23, 2013, at 12:27 PM, Michele Rosso <mrosso at uci.edu> wrote:

> The boundary conditions are periodic. 
> The equation I am solving is:
> 
>        div(beta*grad(u))= f
> 
> where beta is 1 inside the gas phase, 0.001 inside the liquid phase and a value in between for the nodes close to the interface.

This is a pretty big jump for geometric MG.  You might try AMG.  I suspect that the geometry is getting more complex as the simulation progresses.  Does the simulation start with both phases?  Also this problem is singular.  You might try projecting out the constant.  It could be that as the geometry gets more complex floating point errors are creeping in and you are getting an effective constant component to your RHS.

> The system matrix is built so to remain symmetric positive defined despite the coefficients.
> 
> Michele
> 
> 
> On 09/23/2013 09:11 AM, Matthew Knepley wrote:
>> On Mon, Sep 23, 2013 at 8:55 AM, Michele Rosso <mrosso at uci.edu> wrote:
>> Hi,
>> 
>> I am successfully using PETSc to solve a 3D Poisson's equation with CG + MG .  Such equation arises from a projection algorithm for a multiphase incompressible flow simulation.
>> I set up the solver  as I was suggested to do in a previous thread (title: "GAMG speed") and run a test case (liquid droplet with surface tension falling under the effect of gravity in a quiescent fluid). 
>> The solution of the Poisson Equation via multigrid is correct but it becomes progressively slower and slower as the simulation progresses (I am performing successive solves) due to an increase in the number of iterations.
>> Since the solution of the Poisson equation is mission-critical, I need to speed it up as much as I can.
>> Could you please help me out with this?
>> 
>> First, what does the coefficient look like?
>> 
>> Second, what are the boundary conditions?
>> 
>>    Matt
>>  
>> I run the test case with the following options: 
>> 
>> -pc_type mg  -pc_mg_galerkin  -pc_mg_levels 5   -mg_levels_ksp_type richardson -mg_levels_ksp_max_it 1 
>> -mg_coarse_pc_type lu   -mg_coarse_pc_factor_mat_solver_package superlu_dist 
>> -log_summary -ksp_view  -ksp_monitor_true_residual  -options_left 
>> 
>> Please find the diagnostic for the final solve in the attached file "final.txt'. 
>> Thank you, 
>> 
>> Michele
>> 
>> 
>> 
>> -- 
>> 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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