1. Discretization and calculation methods
1.1 Discretization of random fields
The discretization of random fields transforms the individual fields into vectors of correlated random variables.
Let ν(x) be a multidimensional random field defined in a domain Ω. The field is considered to be completely described by its meanE(x), its varianceσ 2 (x) and its correlation functionρ(x, x') between two distinct points with coordinates x and x'. Discretizing the fieldv(x) involves replacing it with a random vector v. All existing methods relate v(x) to v, using a linear transformation, so for a Gaussian random field, v is also Gaussian.
There are numerous methods for discretizing random fields
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Discretization and calculation methods
Spectral stochastic finite element method
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