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  1. J

    Positive definite matrix

    I think it depends on the eigenvalues of B if the eigenvalues of B is larger than 1, the statement holds. Otherwise, it does not.
  2. J

    Wave equation

    Actually, u is complex amplitude of the wave, which denotes the amplitude of given spatial point and time. So u represents the wave field distribution in space.
  3. J

    Galerkin method for wave equation

    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...
  4. J

    Galerkin method for wave equation

    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...