A comparison of matrix-free isogeometric Galerkin and collocation methods for Karhunen--Loève expansion

Numerical computation of the Karhunen--Loève expansion is computationally challenging in terms of both memory requirements and computing time. We compare two state-of-the-art methods that claim to efficiently solve for the K--L expansion: (1) the matrix-free isogeometric Galerkin method using interpolation based quadrature proposed by the authors in [1] and (2) our new matrix-free implementation of the isogeometric collocation method proposed in [2]. Two three-dimensional benchmark problems indicate that the Galerkin method performs significantly better for smooth covariance kernels, while the collocation method performs slightly better for rough covariance kernels.

No reviews yet.

No comments yet.