Generate FEM-based Random Fields

Hi everyone,

as you can read in the title, I am interested in generating FEM-based random fields. That is, employing a finite element mesh to compute the matrices that conform the eigenvalue problem:


where C is the correlation matrix, A is the matrix containing the eigenvalues and B is a matrix obtained by evaluating the finite elements shape functions. Finally, D contains the eigenvectors.

My question is related to the solution of this algebraic problem. Do any of you know if is needed to apply the boundary conditions of the structure that I am analysing or I can solve the problem straightforwardly?

Thanks for your help!