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Poisson PDE discretisation help!

  1. Jan 18, 2014 #1
    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
     
  2. jcsd
  3. Jan 18, 2014 #2
    You evaluate f(x,y) at each center point i,j of your 5 point finite difference scheme.

    Chet
     
  4. Jan 19, 2014 #3
    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? :eek:
     
    Last edited: Jan 19, 2014
  5. Jan 19, 2014 #4

    pasmith

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    I don't know what the values in the cells in the diagram are, but I suspect they are values of [itex]u[/itex]. If so, the outermost cells do not give [itex]x[/itex] and [itex]y[/itex] values but the boundary conditions for [itex]u[/itex].
     
  6. Jan 19, 2014 #5
    I agree.

    Chet
     
  7. Jan 19, 2014 #6
    So I'm doing it incorrectly. How do I compute for it?
     
  8. Jan 19, 2014 #7
    Ah wait, nevermind. I think I remembered something. Thanks a lot.
     
  9. Jan 19, 2014 #8
    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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