In this paper the generation of random fields when the domain is much larger than the characteristic correlation length is made using an adaptation of the Karhunen–Loève expansion (KLE). The KLE requires the computation of the eigen-functions and the eigen-values of the covariance operator for its modal representation. This step can be very expensive if the domain is much larger than the correlation length. To deal with this issue, the domain is split in sub-domains where this modal decomposition can be comfortably computed. The random coefficients of the KLE are conditioned in order to guarantee the continuity of the field and a proper representation of the covariance function on the whole domain. This technique can also be parallelized and applied for non-stationary random fields. Some numerical studies, with different correlation functions and lengths, are presented.

中文翻译：

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使用局部Karhunen-Loève展开生成大规模随机场

在本文中，通过使用Karhunen-Loève展开（KLE）的适应，当域远大于特征相关长度时生成随机场。KLE需要模态表示的协方差算子的特征函数和特征值的计算。如果域远大于相关长度，则此步骤可能会非常昂贵。为了解决此问题，将域划分为多个子域，可以轻松计算此模态分解。对KLE的随机系数进行条件调整，以确保场的连续性并在整个域上正确表示协方差函数。该技术也可以并行化，并应用于非平稳随机场。一些数值研究