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Thread: Analytical solution of the poisson equation

  1. #1
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    Analytical solution of the poisson equation

    Hi,

    Does anyone know how to solve the following for an analytical solution?

    - nabla . sigma (u) = f

    if

    u = sin(pi*x)sin(pi*y)
    v = sin(pi*x)sin(pi*y)

    ?
    I know that I need to assign a value for u and v and then get values of x and y, but I'm not sure what to do afterwards!

    Many thanks !
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  2. #2
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    Re: Analytical solution of the poisson equation

    Quote Originally Posted by mojojojo17 View Post
    Hi,
    Does anyone know how to solve the following for an analytical solution?
    - nabla . sigma (u) = f
    if u = sin(pi*x)sin(pi*y)[ v = sin(pi*x)sin(pi*y)?
    I know that I need to assign a value for u and v and then get values of x and y, but I'm not sure what to do afterwards!
    Please post the entire original question. It is difficult to follow your interruption of it.
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  3. #3
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    Re: Analytical solution of the poisson equation

    Sorry!

    I was mainly looking for information on how to solve an elliptic PDE of the form
    - nabla . sigma (u) = f
    with the assigned values of u. (ignore the v for now)
    so I would give a value to u, then find my x and y from u = sin(pi*x)sin(pi*y)
    then, I would be able to find a value of f from that.
    It is this step that I am confused about.
    Sorry for any confusion in the above post!
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