[CIG-SHORT] nondimensionalization question

[Matthew Knepley]

On Mon, Aug 20, 2012 at 7:19 PM, Lucas Abraham Willemsen
<lawillem at mit.edu>wrote:

>  Hi,
>
> In preparation for my research I am currently investigating the
> nondimensionalization implementation in Pylith. The way I understand things
> is that nondimensionalization should have no effect as long as the double
> precision is good enough in preventing round-off errors. I used a dynamic
> simulation with a
>

This is not the whole story. First, you are not just competing against
roundoff error, but also truncation error, and these
errors can be inflated by the condition number of your problem, so poor
scaling can result in very wrong answers. Second,
poor scaling can result in very poor solver performance as well.


> slip-weakening fault in order to test this theory. When I use a dynamic
> nondimensionalization object everything is as expected. Changing the scales
> 'shear_wave_speed', 'mass_density' and 'wave_period' has no effect on the
> final displacement.
>
> I was told (maybe in error?) that both dynamic and quasistatic
> nondimensionazation objects are valid in a dynamic simulation and should
> give the same result (they do the same thing?).  But when I test this it
> does not work. changing any of the scales in the quasistatic
> nondimensionalization object changes the final displacements significantly
> (orders of magnitude).
>

To make sure that you are doing what you want, you must switch to a direct
solver. In this case, it means
using FieldSplit, full Schur factorization, LU for the displacements, and a
very low tolerance (1e-12 or so)
for the fault tractions. We should definitely make an options file for
these choices. With these, we will know
whether solver convergence is influencing your results.

   Matt


> I browsed around in the source code for the implementations of the objects
> and I found this. It does seem like both these objects essentially do the
> same thing (except for the fact that the quasistatic object will always
> have a default density scale since it is intended for quasistatic
> problems).
>
>
> http://geodynamics.org/svn/cig/cs/spatialdata/tags/v0.5.2/spatialdata/units/NondimElasticDynamic.py
>
> http://geodynamics.org/svn/cig/cs/spatialdata/tags/v0.5.2/spatialdata/units/NondimElasticQuasistatic.py
>
> (it says v0.5.2 in the link, but there is no higher one. Is this what is
> currently used? Could not find the files in the source code download)
>
> A test project can be found here:
> http://web.mit.edu/lawillem/www/nondimtest.zip
>
> Note how changing the dynamic scales changes nothing, while the
> quasistatic ones do influence the final displacements significantly.
>
> best,
> Lucas
>
> P.S. My motivation for this question is that I plan to investigate the
> difference between a quasi-static and dynamic simulation with rate and
> state friction. In order to make the transition from dynamic to real
> quasistatic (implicit formulation) I first wanted to change the
> nondimensionalization object to quasistatic (while problem remains dynamic,
> explicit timestep) and get the same results.
>
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>


-- 
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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