A  Low Rank Tensor Approach for Nonlinear Vlasov Simulations - presented by Prof. Jingmei Qiu

A Low Rank Tensor Approach for Nonlinear Vlasov Simulations

Prof. Jingmei Qiu

Prof. Jingmei Qiu
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A Low Rank Tensor Approach for Nonlinear Vlasov Simulations
Prof. Jingmei Qiu
Jingmei Qiu
University of Delaware
Journal of Computational Physics

Associated Journal of Computational Physics article

W. Guo and J. Qiu (2022) A low rank tensor representation of linear transport and nonlinear Vlasov solutions and their associated flow maps. Journal of Computational Physics
Article of record

In this work, we present a low-rank tensor approach for approximating solutions to the nonlinear Vlasov equation. Our method takes advantage of the tensor-friendly nature of the differential operators in the Vlasov equation to dynamically and adaptively construct a low-rank solution basis through the discretization of the equation and an SVD-type truncation procedure. We utilize finite difference WENO and discontinuous Galerkin spatial discretizations, along with a second-order strong stability preserving multi-step time discretization. To preserve conservation properties, we develop low-rank schemes with local mass, momentum, and energy conservation for the corresponding macroscopic equations. The mass and momentum are conserved using a conservative SVD truncation, while the energy is conserved by replacing the energy component of the kinetic solution with one obtained from a conservative scheme for the macroscopic energy equation. We employ hierarchical Tucker decomposition for high-dimensional problems, and demonstrate the high-order convergence, efficiency, and local conservation properties of our algorithm through a series of linear and nonlinear Vlasov examples.

References
  • 1.
    W. Guo and J. Qiu (2022) A low rank tensor representation of linear transport and nonlinear Vlasov solutions and their associated flow maps. Journal of Computational Physics
Grants
    Air Force Office of Scientific ResearchFA9550-22-1-0390National Science FoundationNSF-DMS-2111253U.S. Department of EnergyDE-SC0023164
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Journal of Computational Physics
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J. Qiu (2023, September 25), A Low Rank Tensor Approach for Nonlinear Vlasov Simulations
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