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!


Hi Alberto,

it’s been a while… Have you figured out an answer to your question? If yes, what is the answer? :slight_smile:

If not, maybe you could give us a bit more information about your problem. What role does the random field have in your problem, and what properties does it have (Gaussian…?) Does this eigenvalue problem come from solving the integral eigenvalue problem of a Karhunen-Loève expansion? Are the boundary conditions for the structure or for the random field?

Hi @nluethen,

sadly I didn’t figure out the answer, but looking at the literature related to my research topic I didn’t need to generate 3D (in the sense that it considers all the integration points of the structure) random fields.

Just to answer your questions quickly:

  • I am trying to model defects that appear in structures made out of composite materials. I finally managed to use 2D stochastic fields, using the analytical formulae of the Karhunen-Loève expansion (KLE). As you may guess, I was considering Gaussian random fields. Please, let me know if there exist such analytical formulae for Lognormal random fields :slight_smile:

  • Yes, I was trying to solve the integral eigenvalue problem of a KLE.

  • Also, I was referring to the boundary conditions of the structure. I guess they are not necessary when imposing the kind of uncertainty I’m dealing with.

Thanks for your interest and your reply. Also for your great toolbox!