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Near-boundary error reduction with an optimized weighted Dirichlet-Neumann boundary condition for stochastic PDE-based Gaussian random field generators

Ricketts, Evan John ORCID: https://orcid.org/0000-0001-8056-070X, Cleall, Peter John ORCID: https://orcid.org/0000-0002-4005-5319, Jefferson, Tony ORCID: https://orcid.org/0000-0002-2050-2521, Kerfriden, Pierre and Lyons, Paul 2023. Near-boundary error reduction with an optimized weighted Dirichlet-Neumann boundary condition for stochastic PDE-based Gaussian random field generators. Engineering with Computers 39 , pp. 3821-3833. 10.1007/s00366-023-01819-6

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Abstract

Random field generation through the solution of stochastic partial differential equations is a computationally inexpensive method of introducing spatial variability into numerical analyses. This is particularly important in systems where material heterogeneity has influence over the response to certain stimuli. Whilst it is a convenient method, spurious values arise in the near boundary of the domain due to the non-exact nature of the specific boundary condition applied. This change in the correlation structure can amplify or dampen the system response in the near-boundary region depending on the chosen boundary condition, and can lead to inconsistencies in the overall behaviour of the system. In this study, a weighted Dirichlet–Neumann boundary condition is proposed as a way of controlling the resulting structure in the near-boundary region. The condition relies on a weighting parameter which scales the application to have a more dominant Dirichlet or Neumann component, giving a closer approximation to the true correlation structure of the Matérn autocorrelation function on which the formulation is based on. Two weighting coefficients are proposed and optimal values of the weighting parameter are provided. Through parametric investigation, the weighted Dirichlet–Neumann approach is shown to yield more consistent correlation structures than the common boundary conditions applied in the current literature. We also propose a relationship between the weighting parameter and the desired length-scale parameter of the field such that the optimal value can be chosen for a given problem.

Item Type: Article
Date Type: Publication
Status: Published
Schools: Engineering
Publisher: Springer Verlag
ISSN: 0177-0667
Date of First Compliant Deposit: 11 April 2023
Date of Acceptance: 3 April 2023
Last Modified: 15 Jan 2024 11:02
URI: https://orca.cardiff.ac.uk/id/eprint/158544

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