2023/05/18 by Egor Kornev, Kornev, Egor, Sergey Dolgov +9 · 9 citations
Computer Science · Mathematics · #Computational Physics and Python Applications #FOS: Mathematics #FOS: Physical sciences #Fluid Dynamics (physics.flu-dyn) #Numerical Analysis (math.NA) #Quantum Physics (quant-ph) #Tensor decomposition and applications
paper · pdf · doi:10.48550/arxiv.2305.10784
openalex publication_date 2023/05/18 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
The solution of computational fluid dynamics problems is one of the most computationally hard tasks, especially in the case of complex geometries and turbulent flow regimes. We propose to use Tensor Train (TT) methods, which possess logarithmic complexity in problem size and have great similarities with quantum algorithms in the structure of data representation. We develop the Tensor train Finite Element Method -- TetraFEM -- and the explicit numerical scheme for the solution of the incompressible Navier-Stokes equation via Tensor Trains. We test this approach on the simulation of liquids mixing in a T-shape mixer, which, to our knowledge, was done for the first time using tensor methods in such non-trivial geometries. As expected, we achieve exponential compression in memory of all FEM matrices and demonstrate an exponential speed-up compared to the conventional FEM implementation on dense meshes. In addition, we discuss the possibility of extending this method to a quantum computer to solve more complex problems. This paper is based on work we conducted for Evonik Industries AG.