[CIG-SHORT] nondimensionalization question

[Charles Williams]

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> 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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> 
> 
> -- 
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Charles A. Williams
Scientist
GNS Science
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PO Box 30368
Lower Hutt  5040
New Zealand
ph (office): 0064-4570-4566
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C.Williams at gns.cri.nz

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