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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;

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# Galerkin method for wave equation

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