An Interpolation Method for Karhunen–Loève Expansion of Random Field Discretization

In the context of global mean square error concerning number random variables in representation, Karhunen–Loève (KL) expansion is optimal series method for field discretization. The computational efficiency and accuracy KL are contingent upon accurate resolution Fredholm integral eigenvalue problem (IEVP). paper proposes an interpolation based on different basis functions such as moving least squares (MLS), (LS), finite element (FEM) to solve IEVP. Compared with Galerkin or Legendre polynomials, main advantage that, calculation eigenvalues eigenfunctions one-dimensional fields, matrix containing covariance function only requires a single integral, which less than two-folded by method. effectiveness proposed verified through various examples. Furthermore, polynomial chaos expansion, stochastic analysis two-dimensional regular irregular domains conducted, extended (XFEM) introduced