Award Abstract # 1846854
CAREER: Computational Methods for Multiscale Kinetic Systems: Uncertainty, Non-Locality, and Variational Formulation

NSF Org: DMS
Division Of Mathematical Sciences
Recipient: REGENTS OF THE UNIVERSITY OF MINNESOTA
Initial Amendment Date: January 31, 2019
Latest Amendment Date: May 30, 2023
Award Number: 1846854
Award Instrument: Continuing Grant
Program Manager: Yuliya Gorb
ygorb@nsf.gov
 (703)292-2113
DMS
 Division Of Mathematical Sciences
MPS
 Directorate for Mathematical and Physical Sciences
Start Date: July 1, 2019
End Date: June 30, 2026 (Estimated)
Total Intended Award Amount: $400,001.00
Total Awarded Amount to Date: $400,001.00
Funds Obligated to Date: FY 2019 = $39,769.00
FY 2020 = $65,315.00

FY 2021 = $112,012.00

FY 2022 = $94,662.00

FY 2023 = $88,243.00
History of Investigator:
  • Li Wang (Principal Investigator)
    wangli1985@gmail.com
Recipient Sponsored Research Office: University of Minnesota-Twin Cities
2221 UNIVERSITY AVE SE STE 100
MINNEAPOLIS
MN  US  55414-3074
(612)624-5599
Sponsor Congressional District: 05
Primary Place of Performance: University of Minnesota, School of Mathematics
206 Church Street SE
Minneapolis
MN  US  55455-0488
Primary Place of Performance
Congressional District:
05
Unique Entity Identifier (UEI): KABJZBBJ4B54
Parent UEI:
NSF Program(s): COMPUTATIONAL MATHEMATICS
Primary Program Source: 01001920DB NSF RESEARCH & RELATED ACTIVIT
01002122DB NSF RESEARCH & RELATED ACTIVIT

01002324DB NSF RESEARCH & RELATED ACTIVIT

01002021DB NSF RESEARCH & RELATED ACTIVIT

01002223DB NSF RESEARCH & RELATED ACTIVIT
Program Reference Code(s): 1045, 9263
Program Element Code(s): 127100
Award Agency Code: 4900
Fund Agency Code: 4900
Assistance Listing Number(s): 47.049

ABSTRACT

Kinetic theory has emerged as a critical tool in studying many-particle systems with random motion, which arise widely in plasma physics, semiconductors, animal swarms, nuclear engineering, among many others. It bridges the gap between microscopic particle system and macroscopic continuum description, and therefore is at the core of multiscale modeling. In addition to its multiscale nature, this project intends to advance the understanding and computation of kinetic theory in new, emerging aspects that involve uncertainties, non-localities, and variational formulations. A parallel educational objective is to prepare and train students at all levels for multi-disciplinary research through advanced courses, topic seminars, and summer programs.

The specific aims of the project include: (1) utilize the variational formulation of macroscopic and kinetic equations to develop scalable, structure preserving, mathematically justifiable methods via advanced optimization techniques; (2) design multiscale computational methods for nonlocal interacting kinetic systems, with emphases on nonlocal collision and connection to fractional diffusion; (3) develop robust algorithms for hyperbolic equations with uncertainty, especially in treating discontinuous solutions; (4) study the inverse problem for nonlinear kinetic systems, including stability analysis with varying scales, numerical regularization and algorithms. The proposed activity is on an interdisciplinary topic and of general interest to both computational mathematicians and scientists from other areas. The variational methods provide a new perspective in overcoming difficulties that are shared among most partial differential equation (PDE) models nowadays: multiple scales, high dimensionality and necessity in preserving physical quantities. The research outcome will have an impact on other disciplines including computational optimal transport, optimal control theory, mean field games, and machine learning. The fractional diffusion solvers will be equally applicable to photon transport through cosmic dust or atmosphere, electron beam dose calculation, and other nonlocal PDEs arising in material science, finance, and plasma physics. Uncertainties that are omnipresent in kinetic equations have a profound influence on the solution behavior and must be carefully quantified. The analysis and algorithms investigated through this project, in both forward and inverse setting, will facilitate the understanding of sensitivity in the system under random perturbations, and largely advance the modern design of device with optimal performance.

This award reflects NSF's statutory mission and has been deemed worthy of support through evaluation using the Foundation's intellectual merit and broader impacts review criteria.

PUBLICATIONS PRODUCED AS A RESULT OF THIS RESEARCH

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(Showing: 1 - 10 of 24)
Carrillo, José A. and Craig, Katy and Wang, Li and Wei, Chaozhen "Primal Dual Methods for Wasserstein Gradient Flows" Foundations of Computational Mathematics , 2021 https://doi.org/10.1007/s10208-021-09503-1 Citation Details
Carrillo, Jose A and Hu, Jingwei and Wang, Li and Wu, Jeremy "A particle method for the homogeneous Landau equation" Journal of Computational Physics: X , v.7 , 2020 https://doi.org/10.1016/j.jcpx.2020.100066 Citation Details
Carrillo, José A and Shu, Ruiwen and Wang, Li and Xu, Wuzhe "To blow-up or not to blow-up for a granular kinetic equation" Physica D: Nonlinear Phenomena , v.470 , 2024 https://doi.org/10.1016/j.physd.2024.134410 Citation Details
Carrillo, José A and Wang, Li and Wei, Chaozhen "Structure Preserving Primal Dual Methods for Gradient Flows with Nonlinear Mobility Transport Distances" SIAM Journal on Numerical Analysis , v.62 , 2024 https://doi.org/10.1137/23M1562068 Citation Details
Carrillo, Jose A. and Wang, Li and Xu, Wuzhe and Yan, Ming "Variational Asymptotic Preserving Scheme for the Vlasov--Poisson--Fokker--Planck System" Multiscale Modeling & Simulation , v.19 , 2021 https://doi.org/10.1137/20M1350431 Citation Details
Chen, Yun and Luo, Rui and Wang, Li and Lee, Sungyon "Self-similarity in particle accumulation on the advancing meniscus" Journal of Fluid Mechanics , v.925 , 2021 https://doi.org/10.1017/jfm.2021.647 Citation Details
Craig, Katy and Liu, Jian-Guo and Lu, Jianfeng and Marzuola, Jeremy L. and Wang, Li "A proximal-gradient algorithm for crystal surface evolution" Numerische Mathematik , v.152 , 2022 https://doi.org/10.1007/s00211-022-01320-0 Citation Details
Einkemmer, Lukas and Li, Qin and Wang, Li and Yunan, Yang "Suppressing instability in a VlasovPoisson system by an external electric field through constrained optimization" Journal of Computational Physics , v.498 , 2024 https://doi.org/10.1016/j.jcp.2023.112662 Citation Details
James, Richard D and Qi, Kunlun and Wang, Li "On the Kinetic Description of the Objective Molecular Dynamics" Multiscale Modeling & Simulation , v.22 , 2024 https://doi.org/10.1137/23M1596727 Citation Details
Lee, Wonjun and Wang, Li and Li, Wuchen "Deep JKO: time-implicit particle methods for general nonlinear gradient flows" Journal of Computational Physics , 2024 https://doi.org/10.1016/j.jcp.2024.113187 Citation Details
Li, Qin and Newton, Kit and Wang, Li "Bayesian Instability of Optical Imaging: Ill Conditioning of Inverse Linear and Nonlinear Radiative Transfer Equation in the Fluid Regime" Computation , v.10 , 2022 https://doi.org/10.3390/computation10020015 Citation Details
(Showing: 1 - 10 of 24)

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