Which Values of x and y Should I Use for Poisson PDE Discretisation?

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Discussion Overview

The discussion revolves around the discretization of the Poisson equation, specifically focusing on how to evaluate the function f(x,y) within the context of a finite difference scheme. Participants explore the appropriate values of x and y to use based on a provided diagram, while also addressing potential misunderstandings in the setup.

Discussion Character

  • Exploratory
  • Technical explanation
  • Homework-related

Main Points Raised

  • One participant describes the Poisson equation and their approach to discretizing the partial derivatives using Taylor series, but expresses uncertainty about how to handle f(x,y).
  • Another participant suggests evaluating f(x,y) at the center points of the finite difference grid.
  • There is a question about which specific x and y values to use from the diagram, with references to values of 30 and 100 for x, and 50 and 100 for y.
  • A participant expresses confusion about the values in the diagram, suspecting they represent boundary conditions rather than the values of x and y.
  • One participant acknowledges a misunderstanding and seeks clarification on how to compute the values correctly.
  • Later, a participant indicates they have recalled the necessary information and expresses relief at resolving their confusion.

Areas of Agreement / Disagreement

Participants do not reach a consensus on the specific values of x and y to use, and there is ongoing uncertainty regarding the interpretation of the diagram and the boundary conditions.

Contextual Notes

The discussion highlights limitations in understanding the diagram and the relationship between the grid points and boundary conditions, which remain unresolved.

maistral
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Okay, I'm trying to play around again :D

A little overview; I know that the Poisson equation is supposed to be:
uxx + uyy = f(x,y)

I can manage to discretise the partial derivative terms by Taylor. I don't know how to deal with the f(x,y) though. Say for example, uxx + uyy = -exp(x). what values of x will I use?

If possible, by virtue of this Laplace equation solution diagram,

https://fbcdn-sphotos-b-a.akamaihd.net/hphotos-ak-prn2/q71/1533880_710799648952993_1272413896_n.jpg

which values of x will I use, is it the 30's or the 100's? If I add y in f(x,y) as well (perhaps changing the equation to -exp(x+y) as an example), which values of y should I use? is it the 50's or the 100s at the right side? Thanks a lot. :D
 
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You evaluate f(x,y) at each center point i,j of your 5 point finite difference scheme.

Chet
 
Chestermiller said:
You evaluate f(x,y) at each center point i,j of your 5 point finite difference scheme.

Chet

If I'm correct (hopefully) you meant that I should evaluate f(x,y) given the (x,y) values of the point in the grid, yes?

But which x and y values should I use; for x in the diagram there's 30 and 100, for y there's 50 and 100? :|

https://fbcdn-sphotos-d-a.akamaihd.net/hphotos-ak-prn2/t1/1551523_711126242253667_2047676360_n.jpg

Or am I doing it incorrectly? :o
 
Last edited:
maistral said:
If I'm correct (hopefully) you meant that I should evaluate f(x,y) given the (x,y) values of the point in the grid, yes?

But which x and y values should I use; for x in the diagram there's 30 and 100, for y there's 50 and 100? :|

https://fbcdn-sphotos-d-a.akamaihd.net/hphotos-ak-prn2/t1/1551523_711126242253667_2047676360_n.jpg

Or am I doing it incorrectly? :o

I don't know what the values in the cells in the diagram are, but I suspect they are values of u. If so, the outermost cells do not give x and y values but the boundary conditions for u.
 
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pasmith said:
I don't know what the values in the cells in the diagram are, but I suspect they are values of u. If so, the outermost cells do not give x and y values but the boundary conditions for u.
I agree.

Chet
 
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So I'm doing it incorrectly. How do I compute for it?
 
Ah wait, nevermind. I think I remembered something. Thanks a lot.
 
Lol yay alright! I got it. I can't believe I actually forgot something that basic. *ashamed*

Thanks a lot again :D

https://fbcdn-sphotos-f-a.akamaihd.net/hphotos-ak-frc3/t1/q81/s720x720/1538901_711533678879590_913247690_n.jpg
 

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