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

Journal Article · Fri Jul 15 00:00:00 EDT 2016 · Journal of Computational Physics

DOI:https://doi.org/10.1016/J.JCP.2016.04.029· OSTI ID:22572335

Liao, Qifeng ^[1]; Lin, Guang ^[2]

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1. School of Information Science and Technology, ShanghaiTech University, Shanghai 200031 (China)
2. Department of Mathematics & School of Mechanical Engineering, Purdue University, West Lafayette, IN 47907 (United States)

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.

• OSTI ID: 22572335
• Journal Information: Journal of Computational Physics, Vol. 317; Other Information: Copyright (c) 2016 Elsevier Science B.V., Amsterdam, The Netherlands, All rights reserved.; Country of input: International Atomic Energy Agency (IAEA); ISSN 0021-9991
• Country of Publication: United States
• Language: English

Related Subjects

71 CLASSICAL AND QUANTUM MECHANICS
GENERAL PHYSICS
ACCURACY
PARTIAL DIFFERENTIAL EQUATIONS
RANDOMNESS
STOCHASTIC PROCESSES