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

Guanjie Wang and Qifeng Liao

Applied Mathematics and Computation, 2024, vol. 463, issue C

Abstract: We present a reduced basis stochastic Galerkin method for partial differential equations with random inputs. In this method, the reduced basis methodology is integrated into the stochastic Galerkin method, resulting in a significant reduction in the cost of solving the Galerkin system. To reduce the main cost of matrix-vector manipulation involved in our reduced basis stochastic Galerkin approach, the secant method is applied to identify the number of reduced basis functions. We present a general mathematical framework of the methodology, validate its accuracy and demonstrate its efficiency with numerical experiments.

Keywords: PDEs with random data; Reduced basis; Generalized polynomial chaos; Stochastic Galerkin method (search for similar items in EconPapers)
Date: 2024
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Persistent link: https://EconPapers.repec.org/RePEc:eee:apmaco:v:463:y:2024:i:c:s0096300323005441

DOI: 10.1016/j.amc.2023.128375

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