A Block Circulant Embedding Method for Simulation of Stationary Gaussian Random Fields on Block-regular Grids

TL;DR

This paper introduces a block circulant embedding method (BCEM) for efficiently sampling stationary Gaussian random fields on irregular grids with block structure, outperforming classical methods that require grid regularization.

Contribution

The paper presents a novel BCEM that handles block-structured irregular grids directly, improving sampling efficiency over traditional regularization-dependent methods.

Findings

BCEM outperforms classical CEM on model problems.

BCEM handles irregular block-structured grids without regularization.

Improved sampling efficiency demonstrated in experiments.

Abstract

We propose a new method for sampling from stationary Gaussian random field on a grid which is not regular but has a regular block structure which is often the case in applications. The introduced block circulant embedding method (BCEM) can outperform the classical circulant embedding method (CEM) which requires a regularization of the irregular grid before its application. Comparison of BCEM vs CEM is performed on some typical model problems.