Galerkin method for wave equation

jvc

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;

defunc

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.

jvc

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!