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Galerkin method for wave equation

  1. Nov 30, 2009 #1

    jvc

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    Hello,

    I want to use Galerkin method to solve 3-D wave equation \nabla^2 u+k^2 u=0, with the following boundary conditions: at z=z_1 plane, u=g, and when x,y,z go to the infinity, u becomes 0.

    My question is how to choose the basis function \phi_n for u: u=\sum \lambda_n \phi_n. As my boudary condition is a little different from the usual setting discussed in many books, I am confused of selecting basis function.

    Best regards;
     
  2. jcsd
  3. Nov 30, 2009 #2
    As long as it forms a basis, I dont think it matters. So the basis functions youre used to should work here as well. I suggest using a weak form if you have Neumann boundaries.
     
  4. Nov 30, 2009 #3

    jvc

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    Thank you for your reply!

    I indeed want to solve it in the weak form. Actually, my problem is to solve wave equation (homogenuous equation) with non-homogenuous boundary conditions, maybe it is Dirichlet problem. Of course, it can be switched to non-homogeneous equation with homogenuous boundary condition.

    The main difficulty I encountered is this problem is of 3-D problem, where weak form is difficult to solve: calculating gradient of 3-D function, and then calculating the inner product in the space defined are not so easy. So I need to choose simple basis function that can be easily calculated with respect to gradient and inner product.

    Anyone has similar experience? Thanks a lot!
     
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