[CIG-SHORT] nondimensionalization question

Mon Aug 20 19:17:07 PDT 2012

Hi Charles,

The layout of the files you linked is different, but it seems like they apply the scales in the same way. The behavior of the quasistatic nondimensionalization object seems to be strange, at least when a dynamic problem is used. The test case I presented was using Pylith 1.7.1 by the way.

best,
Lucas
________________________________
From: Charles Williams [willic3 at gmail.com]
Sent: Monday, August 20, 2012 22:07
To: Matthew Knepley
Cc: Lucas Abraham Willemsen; cig-short at geodynamics.org
Subject: Re: [CIG-SHORT] nondimensionalization question

Also, try looking in the trunk, which is the current implementation.  I'm not sure how much might have changed:

http://geodynamics.org/svn/cig/cs/spatialdata/trunk/spatialdata/units/

Cheers,
Charles

On 21/08/2012, at 1:21 PM, Matthew Knepley wrote:

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