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Advanced Modeling and Simulation in Engineering Sciences

Table 3 Numerical complexity of the standard KLE and the conditioned KLE

From: Large scale random fields generation using localized Karhunen–Loève expansion

Operation

Standard KLE

Conditioned KLE

Kernel modal decomposition

\(\mathcal {O}((n_sM)^3d)\)

\(\mathcal {O}(n_s^3d)\)

Conditioning matrices computation

–

\(\mathcal {O}(\bar{N}^3d)\)

Random field sampling

\(\mathcal {O}(n_s^dM^{d+1}\bar{N})\)

\(\mathcal {O}((n_sM)^d\bar{N})\)

  1. Tensorizable covariance kernel. \(n_s\) number of discretization steps of a segment of length L, M number of prolongations in one direction, d dimension, \(\bar{N}\) maximal number of retained KLE terms among all the directions (dimensions) for \(M=1\)
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