At the tensor4all community, we will host an online talk by Prof. Engin Danis on January 20th at 8:00 AM (Eastern Time)
(14:00 CET / 22:00 JST).
The Zoom link will be distributed via the tensor4all Google Groups (https://tensor4all.org).
Title: "Tensor-Train Finite Difference Method for Compressible Flows”
Abstract:
In this talk, we present tensor-train (TT) finite-difference WENO/TENO methods for solving the compressible Euler equations. We describe how the governing equations are cast in TT format and how TT cross interpolation is used for numerical flux evaluation and high-order WENO/TENO reconstruction. To maintain efficiency and prevent uncontrolled growth of TT ranks, we introduce a dynamic error-estimation strategy that guides rank adaptation and, in turn, controls the overall numerical error of the TT-based scheme. We demonstrate that the TT WENO/TENO approach retains the standard fifth-order accuracy on smooth problems while capturing complex shock structures directly in TT format. Finally, we compare performance against conventional WENO/TENO solvers and show speedups of up to 1000x for low-rank problems.
Related references:
* Danis, M. E., Truong, D., Boureima, I., Korobkin, O., Rasmussen, K. Ø., & Alexandrov, B. S. (2025). Tensor-train WENO scheme for compressible flows. Journal of Computational Physics, 529, 113891. https://doi.org/10.1016/j.jcp.2025.113891
* Danis, E., Truong, D., Boureima, I., Korobkin, O., Rasmussen, K. Ø., & Alexandrov, B. S. (2025). Tensor-train TENO scheme for compressible flows. In AIAA SCITECH 2025 Forum (AIAA Paper 2025-0304). American Institute of Aeronautics and Astronautics. https://doi.org/10.2514/6.2025-0304
* Oseledets, I. V. (2011). Tensor-train decomposition. SIAM Journal on Scientific Computing, 33(5), 2295–2317. https://doi.org/10.1137/090752286
* Jiang, G.-S., & Shu, C.-W. (1996). Efficient implementation of weighted ENO schemes. Journal of Computational Physics, 126, 202–228. 4. https://doi.org/10.1006/jcph.1996.0130
* Fu, L., Hu, X. Y., & Adams, N. A. (2016). A family of high-order targeted ENO schemes for compressible-fluid simulations. Journal of Computational Physics, 305, 333–359. https://doi.org/10.1016/j.jcp.2015.10.037