Reduced basis stochastic Galerkin methods for partial differential equations with random inputs

Wang, Guanjie; Liao, Qifeng

doi:10.1016/j.amc.2023.128375

Applied Mathematics and Computation

2024

DOI: 10.1016/j.amc.2023.128375

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Reduced basis stochastic Galerkin methods for partial differential equations with random inputs

Guanjie Wang,

Qifeng Liao

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Cited by 2 publications

References 27 publications

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Random field of homogeneous and multi-material structures by the smoothed finite element method and Karhunen–Loève expansion

Cao,

Han,

et al. 2024

Engineering Analysis with Boundary Elements

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Random field of homogeneous and multi-material structures by the smoothed finite element method and Karhunen–Loève expansion

Cao,

Han,

et al. 2024

Engineering Analysis with Boundary Elements

View full text Add to dashboard Cite

Semi-Intrusive Stochastic Galerkin Finite Element Method for Adjoint-Based Optimization Under Uncertainty

Boopathy,

Kennedy

2024

Journal of Aerospace Information Systems

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The stochastic Galerkin method for the propagation of probabilistically modeled uncertainties can be difficult to apply in practice due to its formulation and the challenge of creating a computational infrastructure to support it. To address these challenges, this work proposes a sampling-based stochastic Galerkin method that leverages existing deterministic analysis and adjoint-based derivative implementations. The proposed formulation is semi-intrusive since it is implemented using an existing deterministic framework, requiring only the numerical sampling of the deterministic residuals, Jacobians, boundary conditions, and adjoint implementations at nodes in the probabilistic domain. The software architectures to support stochastic generalizations of the deterministic finite element frameworks are presented. This proposed approach is demonstrated using a finite element framework for flexible multibody dynamics problems. Finally, the semi-intrusive implementation of the stochastic Galerkin method is used to demonstrate gradient-based optimizations of flexible multibody dynamics systems in the presence of probabilistically modeled uncertainties.

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Reduced basis stochastic Galerkin methods for partial differential equations with random inputs

Cited by 2 publications

References 27 publications

Random field of homogeneous and multi-material structures by the smoothed finite element method and Karhunen–Loève expansion

Random field of homogeneous and multi-material structures by the smoothed finite element method and Karhunen–Loève expansion

Semi-Intrusive Stochastic Galerkin Finite Element Method for Adjoint-Based Optimization Under Uncertainty

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