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An algorithm is developed for generating samples of vector-valued Gaussian processes and fields. The algorithm is based on Karhunen–Loève (KL) representations of vector-valued random functionsZ  ⁢   (  x  ){Z(x)}    with finite variances and their construction involves two steps. First, truncation levels{   m  i   }{\{m_{i}\}}    are selected for the KL representations of the components{    Z  i   ⁢   (  x  )    }{\{Z_{i}(x)\}}    ofZ  ⁢   (  x  ){Z(x)}    such that they meet imposed accuracies. Second, the truncation levels{   m  i   }{\{m_{i}\}}    are accepted or increased if the accuracies of resulting cross correlation functions ofZ  ⁢   (  x  ){Z(x)}    satisfy or violate preset constraints. Theoretical arguments are used to prove the validity of the proposed KL-based models ofZ  ⁢   (  x  ){Z(x)}   . The models are applied to develop an efficient Monte Carlo algorithm for generating samples of vector-valued Gaussian functions. Numerical examples illustrate the implementation of the proposed Monte Carlo algorithm and demonstrate its performance.

Monte Carlo algorithm for vector-valued Gaussian functions with preset component accuracies