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