Abstract Details
Abstracts
Author: Stephen R White
Requested Type: Consider for Invited
Submitted: 2026-03-27 12:16:47
Co-authors: Adam Stanier, Luis Chacon, William Taitano, Rodrigo Jose Gonzalez Hernandez
Contact Info:
Los Alamos National Laboratory
125 Central Park Square
Los Alamos, New Mexico 87545
United States
Abstract Text:
Modeling high temperature plasmas in controlled fusion applications is a grand challenge problem, requiring the multi-scale solution of a high-dimensional (d = 6) kinetic equation. The particle-in-cell (PIC) approach is extremely scalable but suffers from discrete particle noise errors that can severely limit accuracy over long time-scales and present a critical barrier to model certain phenomena with low signal-to-noise. The low rank (LR) approach has shown promise to break the curse of dimensionality in kinetic plasma simulations when the solution can be accurately represented with a LR approximation. eg, the tensor train [1] LR representation can reduce the storage footprint from O(N^d) to O(2Nr + (d-2)Nr^2), for d dimensions with N grid points and rank r. However, such schemes can lose efficiency if the rank grows too large. While this can be mitigated by truncating the LR solution, doing so typically introduces significant conservation errors.
We present a first-of-a-kind implicit and fully conservative LR algorithm to solve the hybrid kinetic-ion fluid-electron plasma model. Our Crank-Nicolson solver conservatively advances the TT solution, and we employ a conservative TT Singular Value Decomposition (TT-SVD) truncation motivated by [2], mitigating conservation errors. We showcase this scheme for several electrostatic and electromagnetic test problems.
Further, we show some initial results of using this LR solver as a control variate solution to reduce noise in an implicit and conservative hybrid-PIC scheme. This combined LR-PIC scheme can overcome limitations associated with the individual LR and PIC schemes - where necessary the rank of the LR control variate solution can be capped for efficiency, while still having significant accuracy to reduce noise in the PIC solver.
References:
[1] Oseledets, Ivan. "Tensor-Train Decomposition."
[2] Guo, W., Qiu, JM. "A Local Macroscopic Conservative (LoMaC) Low Rank Tensor Method for the Vlasov Dynamics."
Characterization: 4.0
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