[CIG-SHORT] Linear Convergence Using SNES

Wed Sep 19 11:04:16 PDT 2012

Hi Brad and Matt,

Thanks for the help and the offer to look over a diagram of my problem.
 I've put together a one page project summary/description with conceptual
and model diagrams of the problem.  If you need a format other than PDF,
just let me know.

Thanks again!
Jeff

On Wed, Sep 19, 2012 at 8:16 AM, Brad Aagaard <baagaard at usgs.gov> wrote:

> Jeff,
>
> Can you send us a diagram of the problem you are trying to solve?
>
> There may be some simple tricks to improving the rate of convergence by
> either adjusting the mesh, domain, and BC.
>
> Brad
>
>
> On 09/18/2012 05:42 PM, Jeffrey Thompson wrote:
>
>> Hi Brad and Matt,
>>
>> Thank you for your rapid responses and suggestions.  I've spent the day
>> looking into things, and here's what I've managed to find out:
>>
>> Brad, in terms of the mesh, I've run a few models with a uniform mesh size
>> over a range of element lengths, and it seems like in each case, there is
>> still only linear convergence, albeit with fewer iterations on each time
>> step as the mesh is made coarser.  However, even at a coarseness beyond a
>> useful level (100 meters spacing, which is not really enough nodes (5) to
>> capture the nature of the applied pressure distribution), I still need 77
>> iterations to converge in the nonlinear solver.  And this is running with
>> the nondimensional scales set equal to the relaxation time, mesh spacing,
>> and shear modulus.  This result leads me to think that the linear nature
>> of
>> the convergence is perhaps not related to the mesh.  However, your points
>> about my mesh are good and the suggestions are certainly useful in terms
>> of
>> reducing the time it takes the model to iterate and ultimately reach
>> convergence.
>>
>> Matt, I was able to import the Jacobian for my problem on the coarsest
>> mesh
>> into matlab to look for singularity.  The matrix is full-rank and
>> invertible.  The calculated condition number from the COND function is
>> 1.7409e+05.  And this problem had linear convergence in the nonlinear
>> solver.
>>
>> Thanks again for looking into this for me and for the suggestions,
>> Jeff
>>
>> On Tue, Sep 18, 2012 at 1:01 PM, Brad Aagaard <baagaard at usgs.gov> wrote:
>>
>>  Jeff,
>>>
>>> I suspect your slow convergence (in addition to any solver settings) is
>>> due to your spatial variation of discretization size. Why do you have
>>> such a fine discretization over the entire middle portion of the domain
>>> and then rapid coarsening right near the top and bottom (+y and -y)
>>> edges? You only need fine resolution where there are large strain
>>> gradients.
>>>
>>> Carrying around so many extra DOF unnecessarily increases the problem
>>> size and then coarsening right at the edges introduces distorted cells
>>> which decreases the rate of convergence.
>>>
>>> The length scale and shear modulus used in the nondimensionalization
>>> should be comparable to the discretization size and shear modulus in
>>> your problem. Picking ones that minimize the minimum residual is
>>> irrelevant. You want the nondimensionalized displacements and stresses
>>> to on the order of 1.0 in order to produce a well-conditioned system.
>>>
>>> Brad
>>>
>>>
>>>
>>>
>>> On 09/18/2012 11:30 AM, Jeffrey Thompson wrote:
>>>
>>>> Hi Cig-Short,
>>>>
>>>> I'm having an issue where I'm only able to achieve a slow rate of linear
>>>> convergence using the nonlinear solver, resulting in prohibitively long
>>>>
>>> run
>>>
>>>> times.  I've attached a tarball with the relevant configuration, mesh,
>>>>
>>> and
>>>
>>>> spatialdb files to run my problem.
>>>>
>>>> The gist of the problem I'm trying run is an extension of the
>>>>
>>> dyke-opening
>>>
>>>> example in the manual, with a horizontal opening under the action of a
>>>> constant pressure (normal traction) distribution between a viscoelastic
>>>>
>>> and
>>>
>>>> elastic layer.  This is a two dimensional model.  I'm using the
>>>> following
>>>> preconditioner scheme to insure rapid convergence of the linear solver
>>>>
>>> (1-2
>>>
>>>> iterations):
>>>>
>>>> [pylithapp.petsc]
>>>> ksp_rtol = 1.0e-15
>>>> pc_type = lu
>>>> sub_pc_factor_shift_positive_**definite = 0
>>>> sub_pc_factor_shift_nonzero =
>>>>
>>>> fs_pc_type = fieldsplit
>>>> fs_pc_fieldsplit_real_diagonal = true
>>>> fs_pc_fieldsplit_type = schur
>>>> fs_pc_fieldsplit_schur_**factorization_type = full
>>>>
>>>> fs_fieldsplit_0_pc_type = lu
>>>> fs_fieldsplit_0_ksp_type = preonly
>>>> fs_fieldsplit_1_pc_type = jacobi
>>>> fs_fieldsplit_1_ksp_type = gmres
>>>> fs_fieldsplit_1_ksp_rtol = 1.0e-15
>>>> fs_fieldsplit_2_pc_type = jacobi
>>>> fs_fieldsplit_2_ksp_type = gmres
>>>> fs_fieldsplit_2_ksp_rtol = 1.0e-15
>>>> fs_fieldsplit_3_pc_type = jacobi
>>>> fs_fieldsplit_3_ksp_type = gmres
>>>> fs_fieldsplit_3_ksp_rtol = 1.0e-15
>>>>
>>>> log_summary = true
>>>> ksp_max_it = 100
>>>> ksp_gmres_restart = 50
>>>> ksp_converged_reason = true
>>>>
>>>> snes_ls_monitor = true
>>>> snes_rtol = 1.0e-8
>>>> snes_atol = 1.0e-7
>>>> snes_max_it = 10000
>>>> snes_monitor = true
>>>> snes_converged_reason = true
>>>>
>>>> However, as I mentioned earlier, the SNES residual only drops linearly
>>>>
>>> with
>>>
>>>> the default solving scheme past the first SNES iteration.  I've tried
>>>>
>>> using
>>>
>>>> different PETSc options for SNES, but none of the scheme I've tried had
>>>> better results (and many were worse or never converged).  To summarize
>>>> these attempts:
>>>> NGMRES: did not converge (residual remained constant)
>>>> NCG: Tried the 5 different flavours, all either diverged or never
>>>>
>>> converged
>>>
>>>> (bounced between a few residuals)
>>>> other LINESEARCH options: none were as good as the default behavior
>>>>
>>>> I've also tried different non-dimensionalization options and found a set
>>>> that gives the optimal initial residual (i.e., the lowest value of SNES
>>>> residual number 0).  It seems like for this problem, only the
>>>> nondimensional length-scale directly impacts the SNES residual.
>>>>
>>>> The result of all of this is that I currently need around 800-1000
>>>> non-linear iterations to converge on a single time-step at best.  I have
>>>>
>>> a
>>>
>>>> feeling that I must be doing something wrong, but I can't tell if this
>>>>
>>> is a
>>>
>>>> solver issue or some other type of problem (bad mesh, poorly defined
>>>> boundary conditions, etc).  Any advice would be appreciated!
>>>>
>>>> Thanks for the help!
>>>> Jeff Thompson
>>>> Caltech Seismolab
>>>>
>>>>
>>>>
>>>> ______________________________**_________________
>>>> CIG-SHORT mailing list
>>>> CIG-SHORT at geodynamics.org
>>>> http://geodynamics.org/cgi-**bin/mailman/listinfo/cig-short<http://geodynamics.org/cgi-bin/mailman/listinfo/cig-short>
>>>>
>>>>
>>> ______________________________**_________________
>>> CIG-SHORT mailing list
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>>>
>>>
>>
>
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