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arXiv · 2607.08936

A Tensor-Train Discontinuous Galerkin Method for the Vlasov-Maxwell System

Rujeko Chinomona·Dibyendu Adak·William J. Barham·Duc P. Truong·Nathan V. Roberts·Kim Ø. Rasmussen·Boian S. Alexandrov
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Abstract

We present a tensor-train discontinuous Galerkin (TT-DG) formulation for the Vlasov--Maxwell system that combines a modal DG discretization with low-rank tensor representations of the phase-space solution and discrete operators. The formulation exploits the tensor-product structure of the DG discretization to perform quadrature, differentiation, nonlinear upwind flux evaluation, and time integration directly in compressed form. The method is evaluated on several standard 1D2V Vlasov--Maxwell benchmark problems, including the streaming Weibel instability, weak Landau damping, and two-stream instability problems. Across these problems, the TT formulation reproduces the accuracy and conservation behavior of the underlying full-grid DG discretization while substantially reducing memory usage and runtime. For weakly nonlinear problems, compression ratios exceeding $10^4$ are obtained together with significant speedups relative to the full-grid solver. For the strongly nonlinear two-stream instability problem, the TT formulation remains effective despite reduced compressibility caused by fine-scale phase-space filamentation. These results demonstrate that tensor-train representations provide an effective approach for reducing the computational cost of deterministic DG-based kinetic plasma simulations while retaining the favorable numerical properties of the underlying discretization.

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Rujeko Chinomona, Dibyendu Adak, William J. Barham, Duc P. Truong, Nathan V. Roberts, Kim Ø. Rasmussen, Boian S. Alexandrov. 2026-07-09. A Tensor-Train Discontinuous Galerkin Method for the Vlasov-Maxwell System. https://arxiv.org/abs/2607.08936

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