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DOE OSTI · 22572335

Reduced basis ANOVA methods for partial differential equations with high-dimensional random inputs

Liao, Qifeng·Lin, Guang
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Abstract

In this paper we present a reduced basis ANOVA approach for partial deferential equations (PDEs) with random inputs. The ANOVA method combined with stochastic collocation methods provides model reduction in high-dimensional parameter space through decomposing high-dimensional inputs into unions of low-dimensional inputs. In this work, to further reduce the computational cost, we investigate spatial low-rank structures in the ANOVA-collocation method, and develop efficient spatial model reduction techniques using hierarchically generated reduced bases. We present a general mathematical framework of the methodology, validate its accuracy and demonstrate its efficiency with numerical experiments.

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71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSICSACCURACYPARTIAL DIFFERENTIAL EQUATIONSRANDOMNESSSTOCHASTIC PROCESSES

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Liao, Qifeng, Lin, Guang. 2016-07-15. Reduced basis ANOVA methods for partial differential equations with high-dimensional random inputs. https://doi.org/10.1016/j.jcp.2016.04.029

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