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

2022/09/25 by Guanjie Wang, Wang, Guanjie, Qifeng Liao +1 · 1 citation
Computer Science · Decision Sciences · Environmental Science · #Matrix Theory and Algorithms #Probabilistic and Robust Engineering Design #Soil Geostatistics and Mapping

paper · pdf · doi:10.48550/arxiv.2209.12163

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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