Journal article
A bi-fidelity stochastic collocation method for transport equations with diffusive scaling and multi-dimensional random inputs
Journal of computational physics, Vol.462, 111252
08/01/2022
DOI: 10.1016/j.jcp.2022.111252
Abstract
•Develop a bi-fidelity method for linear transport equations with random parameters.•Employ the Goldstein-Taylor as low-fidelity model to accelerate convergence of the scheme.•The first work to apply multi-fidelity approach to kinetic equations under the diffusive scaling.
In this paper, we consider the development of efficient numerical methods for linear transport equations with random parameters and under the diffusive scaling. We extend to the present case the bi-fidelity stochastic collocation method introduced in [33,50,51]. For the high-fidelity transport model, the asymptotic-preserving scheme [29] is used for each stochastic sample. We employ the simple two-velocity Goldstein-Taylor equation as low-fidelity model to accelerate the convergence of the uncertainty quantification process. The choice is motivated by the fact that both models, high fidelity and low fidelity, share the same diffusion limit. Speed-up is achieved by proper selection of the collocation points and reasonable approximation of the high-fidelity solution. Extensive numerical experiments are conducted to show the efficiency and accuracy of the proposed method, even in non diffusive regimes, with empirical error bound estimations as studied in [16].
Details
- Title: Subtitle
- A bi-fidelity stochastic collocation method for transport equations with diffusive scaling and multi-dimensional random inputs
- Creators
- Liu Liu - Chinese University of Hong KongLorenzo Pareschi - University of FerraraXueyu Zhu - Department of Mathematics, University of Iowa, Iowa City, IA 52242, USA
- Resource Type
- Journal article
- Publication Details
- Journal of computational physics, Vol.462, 111252
- DOI
- 10.1016/j.jcp.2022.111252
- ISSN
- 0021-9991
- eISSN
- 1090-2716
- Publisher
- Elsevier Inc
- Grant note
- DOI: 10.13039/100017142, name: Gruppo Nazionale per il Calcolo Scientifico; DOI: 10.13039/501100002920, name: Research Grants Council, University Grants Committee; DOI: 10.13039/100000893, name: Simons Foundation, award: 504054; DOI: 10.13039/501100003407, name: Ministero dell’Istruzione, dell’Università e della Ricerca, award: 2017KKJP4X; DOI: 10.13039/501100004853, name: Chinese University of Hong Kong; DOI: 10.13039/100009112, name: Istituto Nazionale di Alta Matematica "Francesco Severi"
- Language
- English
- Date published
- 08/01/2022
- Academic Unit
- Mathematics
- Record Identifier
- 9984258365702771
Metrics
32 Record Views