[pooma-dev] ?

[Jeffrey D. Oldham]

Roman Krylov wrote:

> I'm sorry, I merely copied/pasted it from  
> http://www.zib.de/benger/pooma/tut-01.html#laplace
> So,... is it proposal to change that  tutorial?
> But the question persists:
>     how a metal sheet could have non-constant(spatially) electric 
> potential distribution whereas it should be constant V=const ?
> Cheers
>    Roman.
>
>>
>> Would this text be more acceptable:
>> "... where V is, for example, the electric potential of a charge-free 
>> flat metal sheet"?
>>
Yes, we can change the tutorial text if that clarifies the text for you.

In case it does not, let me try to explain some reasons for presenting 
the charge-free equation in a different way.  I do understand that a 
charge-free region should have a constant voltage.  The tutorial does 
begin with this case but then moves to the case with a non-zero charge 
distribution \Beta.  For this, the voltage should not be constant.

There are several reasons for taking this approach:

1) When introducing a topic, it is usually a good idea to introduce the 
simplest possible case even if it is not particularly interesting in the 
real world.  This permits the person learning the topic to learn a 
simpler case with fewer things to learn at once.  After a simple case is 
learned, it can be made more complicated by gradually adding 
complications.  This gradual approach permits the learner to see how 
each particular addition changes the previous solution.

This approach is taken for this particular POOMA tutorial.  A 
non-physicist, non-computer-scientist has a lot to learn at the 
beginning of the tutorial.  A physicist might be bored by the physics 
but still needs to learn the POOMA toolkit.  A computer scientist has to 
learn some physics to understand the tutorial.  Those who understand 
both physics and computer science are a fortunate few.

2) We cannot rely on POOMA learners to know how to solve the Laplace 
equation for a charge-free region.

3) It is not immediately clear that the proposed solution for the 
charge-free region using POOMA will exactly match the analytical 
solution although, admittedly, it does not require much thought to see 
this.  If there are small numerical inaccuracies, solving the 
charge-free equation using the toolkit will indicate what types of 
inaccuracies occur.  Using this knowledge, one can better understand the 
inaccuracies found when solving the charged-region equation.  (For this 
particular example, I do not explect any inaccuracies, but I might be 
wrong.)


I hope this explains some reasons why the tutorial is presented the way 
it is.  If you wish to have some text changed, please send a recommended 
change that will make sense to people who do not know how to solve the 
charge-free equation and to people who do not know physics.

-- 
Jeffrey D. Oldham
oldham at codesourcery.com