Выходит 6 номеров в год
ISSN Печать: 2152-5080
ISSN Онлайн: 2152-5099
Indexed in
A MULTI-FIDELITY STOCHASTIC COLLOCATION METHOD FOR PARABOLIC PARTIAL DIFFERENTIAL EQUATIONS WITH RANDOM INPUT DATA
Краткое описание
Over the last few years there have been dramatic advances in the area of uncertainty quantification. In particular, we have seen a surge of interest in developing efficient, scalable, stable, and convergent computational methods for solving differential equations with random inputs. Stochastic collocation (SC) methods, which inherit both the ease of implementation of sampling methods like Monte Carlo and the robustness of nonsampling ones like stochastic Galerkin to a great deal, have proved extremely useful in dealing with differential equations driven by random inputs. In this work we propose a novel enhancement to stochastic collocation methods using deterministic model reduction techniques. Linear parabolic partial differential equations with random forcing terms are analysed. The input data are assumed to be represented by a finite number of random variables. A rigorous convergence analysis, supported by numerical results, shows that the proposed technique is not only reliable and robust but also efficient.
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Raissi M., Seshaiyer P., Application of local improvements to reduced-order models to sampling methods for nonlinear PDEs with noise, International Journal of Computer Mathematics, 95, 5, 2018. Crossref
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Skinner Ryan, Doostan Alireza, Peters Eric, Evans John, Jansen Kenneth E., An Evaluation of Multi-Fidelity Modeling Efficiency on a Parametric Study of NACA Airfoils, 35th AIAA Applied Aerodynamics Conference, 2017. Crossref
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Giselle Fernández-Godino M., Park Chanyoung, Kim Nam H., Haftka Raphael T., Issues in Deciding Whether to Use Multifidelity Surrogates, AIAA Journal, 57, 5, 2019. Crossref
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Nguyen Long, Raissi Maziar, Seshaiyer Padmanabhan, Efficient Physics Informed Neural Networks Coupled with Domain Decomposition Methods for Solving Coupled Multi-physics Problems, in Advances in Computational Modeling and Simulation, 2022. Crossref
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Nguyen Long, Raissi Maziar, Seshaiyer Padmanabhan, Modeling, Analysis and Physics Informed Neural Network approaches for studying the dynamics of COVID-19 involving human-human and human-pathogen interaction, Computational and Mathematical Biophysics, 10, 1, 2022. Crossref