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

Guanjie Wang; Qifeng Liao

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arXiv · 2209.12163

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

Guanjie Wang·Qifeng Liao

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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.

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Guanjie Wang, Qifeng Liao. 2022-09-25. Reduced basis stochastic Galerkin methods for partial differential equations with random inputs. https://arxiv.org/abs/2209.12163

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