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Topic: Is this an exceptionally hard set of questions to answer?
Replies: 68   Last Post: Nov 11, 2002 7:54 PM

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Kevin Foltinek

Posts: 680
Registered: 12/8/04
Re: Is this an exceptionally hard set of questions to answer?
Posted: Oct 16, 2002 3:51 PM
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Alberto Moreira <junkmail@moreira.mv.com> writes:

> >Sometimes numerical solutions "blow up" because of instability in the
> >numerical scheme. (To see this for yourself, discretize the heat
> >equation u_t=u_xx,

> [snip]
> One solution is to use simulation, not computation. This is what I've
> been talking about all the time. The final test for an aircraft
> design, before the maiden flight, is the wind tunnel - equations alone
> won't do. Well, we can set up a simulated wind tunnel inside our
> computers, and we don't necessarily need to put in the Navier-Stokes
> equations, either in their closed form or in their numerical form.


If you're going to simulate a wind tunnel in your computer, then you
are doing computation. Whether the computations you do to simulate
your wind tunnel are based on Navier-Stokes or other models is
irrelevant; the numerical stability and accuracy must be estimated if
you want to use the results.

If you're going to build a prototype and put it into a real wind
tunnel, then you're not doing modelling, you're doing prototyping. If
you want to build a model rather than a prototype, then you are doing
modelling, but you had better understand how things change with the
scale, which requires at least a superficial understanding of the
mathematical model.

> Many blowups due to numerical instability can be negotiated by
> increasing the precision.


You obviously did not investigate the heat equation as I suggested you
do. Increasing the precision *cannot* fix the problems caused by
numerical instability. These problems are much more fundamental than
that. (Blindly subdividing the grid into more squares similarly
cannot fix the problems.)

> >This is not directly relevant to a K-12 education discussion, but it
> >does show that raw computational power may not be sufficient to obtain
> >correct answers from a model.

>
> If we had orders of magnitude more computational power than we have
> today, we could perform the numerical method with an
> infinite-precision numerical package written in Lisp:


And if you don't pay attention to the mathematics of numerical
instability, your solution will blow up in just as many steps as when
you perform the same method with single-precision floats on a 1970s
era computer.

Kevin.



Date Subject Author
9/28/02
Read Is this an exceptionally hard set of questions to answer?
Karl M. Bunday
9/30/02
Read Re: Is this an exceptionally hard set of questions to answer?
Alberto C Moreira
9/30/02
Read Re: Is this an exceptionally hard set of questions to answer?
Shmuel (Seymour J.) Metz
10/5/02
Read Re: Is this an exceptionally hard set of questions to answer?
Moufang Loop
10/7/02
Read Re: Is this an exceptionally hard set of questions to answer?
Shmuel (Seymour J.) Metz
9/30/02
Read Re: Is this an exceptionally hard set of questions to answer?
Stephen Herschkorn
9/30/02
Read Re: Is this an exceptionally hard set of questions to answer?
Magi D. Shepley
10/1/02
Read Re: Is this an exceptionally hard set of questions to answer?
Karl M. Bunday
10/2/02
Read Re: Is this an exceptionally hard set of questions to answer?
Kevin Foltinek
10/2/02
Read Re: Is this an exceptionally hard set of questions to answer?
Karl M. Bunday
10/3/02
Read Re: Is this an exceptionally hard set of questions to answer?
Alberto C Moreira
10/3/02
Read Re: Is this an exceptionally hard set of questions to answer?
Kevin Foltinek
10/3/02
Read Re: Is this an exceptionally hard set of questions to answer?
Jim Hunter
10/4/02
Read Re: Is this an exceptionally hard set of questions to answer?
Herman Rubin
10/4/02
Read Re: Is this an exceptionally hard set of questions to answer?
Alberto C Moreira
10/5/02
Read Re: Is this an exceptionally hard set of questions to answer?
Herman Rubin
10/4/02
Read Re: Is this an exceptionally hard set of questions to answer?
Alberto C Moreira
10/4/02
Read Re: Is this an exceptionally hard set of questions to answer?
Kevin Foltinek
10/5/02
Read Re: Is this an exceptionally hard set of questions to answer?
Alberto C Moreira
10/6/02
Read Re: Is this an exceptionally hard set of questions to answer?
Virgil
10/6/02
Read Re: Is this an exceptionally hard set of questions to answer?
Herman Rubin
10/6/02
Read Re: Is this an exceptionally hard set of questions to answer?
Jim Hunter
10/6/02
Read Re: Is this an exceptionally hard set of questions to answer?
Virgil
10/7/02
Read Re: Is this an exceptionally hard set of questions to answer?
Kevin Foltinek
10/8/02
Read Re: Is this an exceptionally hard set of questions to answer?
Alberto C Moreira
10/8/02
Read Re: Is this an exceptionally hard set of questions to answer?
Kevin Foltinek
10/9/02
Read Re: Is this an exceptionally hard set of questions to answer?
Alberto C Moreira
10/10/02
Read Re: Is this an exceptionally hard set of questions to answer?
Kevin Foltinek
10/11/02
Read Re: Is this an exceptionally hard set of questions to answer?
Alberto C Moreira
10/14/02
Read Re: Is this an exceptionally hard set of questions to answer?
Kevin Foltinek
10/15/02
Read Re: Is this an exceptionally hard set of questions to answer?
Alberto C Moreira
10/15/02
Read Re: Is this an exceptionally hard set of questions to answer?
Kevin Foltinek
10/16/02
Read Re: Is this an exceptionally hard set of questions to answer?
Alberto C Moreira
10/16/02
Read Re: Is this an exceptionally hard set of questions to answer?
Kevin Foltinek
10/14/02
Read Re: Is this an exceptionally hard set of questions to answer?
Kevin Foltinek
10/16/02
Read Re: Is this an exceptionally hard set of questions to answer?
Alberto C Moreira
10/16/02
Read Re: Is this an exceptionally hard set of questions to answer?
Kevin Foltinek
10/12/02
Read Re: Is this an exceptionally hard set of questions to answer?
Shmuel (Seymour J.) Metz
10/14/02
Read Re: Is this an exceptionally hard set of questions to answer?
Kevin Foltinek
10/25/02
Read Re: Is this an exceptionally hard set of questions to answer?
Van Bagnol
10/25/02
Read Re: Is this an exceptionally hard set of questions to answer?
Alberto C Moreira
10/26/02
Read Re: Is this an exceptionally hard set of questions to answer?
Van Bagnol
10/27/02
Read Re: Is this an exceptionally hard set of questions to answer?
Alberto C Moreira
10/27/02
Read Re: Is this an exceptionally hard set of questions to answer?
Herman Rubin
10/28/02
Read Re: Is this an exceptionally hard set of questions to answer?
Kevin Foltinek
10/29/02
Read Re: Is this an exceptionally hard set of questions to answer?
Alberto C Moreira
10/24/02
Read Re: Is this an exceptionally hard set of questions to answer?
Van Bagnol
10/25/02
Read Re: Is this an exceptionally hard set of questions to answer?
Van Bagnol
10/26/02
Read Re: Is this an exceptionally hard set of questions to answer?
Alberto C Moreira
10/28/02
Read Re: Is this an exceptionally hard set of questions to answer?
Kevin Foltinek
10/29/02
Read Re: Is this an exceptionally hard set of questions to answer?
Alberto C Moreira
10/29/02
Read Re: Is this an exceptionally hard set of questions to answer?
Kevin Foltinek
10/31/02
Read Re: Is this an exceptionally hard set of questions to answer?
Alberto C Moreira
10/31/02
Read Re: Is this an exceptionally hard set of questions to answer?
Kevin Foltinek
11/2/02
Read Re: Is this an exceptionally hard set of questions to answer?
Alberto C Moreira
11/2/02
Read Re: Is this an exceptionally hard set of questions to answer?
David Redmond
11/3/02
Read Re: Is this an exceptionally hard set of questions to answer?
Alberto C Moreira
11/3/02
Read Re: Is this an exceptionally hard set of questions to answer?
Alberto C Moreira
11/4/02
Read Re: Is this an exceptionally hard set of questions to answer?
Kevin Foltinek
11/2/02
Read Re: Is this an exceptionally hard set of questions to answer?
Virgil
11/4/02
Read Re: Is this an exceptionally hard set of questions to answer?
Kevin Foltinek
11/5/02
Read Re: Is this an exceptionally hard set of questions to answer?
Alberto C Moreira
11/5/02
Read Re: Is this an exceptionally hard set of questions to answer?
Kevin Foltinek
11/6/02
Read Re: Is this an exceptionally hard set of questions to answer?
Alberto C Moreira
11/7/02
Read Re: Is this an exceptionally hard set of questions to answer?
Kevin Foltinek
11/9/02
Read Re: Is this an exceptionally hard set of questions to answer?
Alberto C Moreira
11/11/02
Read Re: Is this an exceptionally hard set of questions to answer?
Kevin Foltinek
10/3/02
Read Re: Is this an exceptionally hard set of questions to answer?
Kevin Foltinek
10/5/02
Read Re: Is this an exceptionally hard set of questions to answer?
Magi D. Shepley

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