Abstract
In this paper, we present a methodology for the numerical solving of partial differential equations in 2D geometries with piecewise smooth boundaries via finite element method (FEM) using a Quantized Tensor Train (QTT) format. During the calculations, all the operators and data are assembled and represented in a compressed tensor format. We introduce an efficient assembly procedure of FEM matrices in the QTT format for curvilinear domains. The features of our approach include efficiency in terms of memory consumption and potential expansion to quantum computers. We demonstrate the correctness and advantages of the method by solving a number of problems, including nonlinear incompressible Navier–Stokes flow, in differently shaped domains.
| Original language | English |
|---|---|
| Article number | 3277 |
| Journal | Mathematics |
| Volume | 12 |
| Issue number | 20 |
| Early online date | 18 Oct 2024 |
| DOIs | |
| Publication status | Published - 18 Oct 2024 |
Data Availability Statement
The original contributions presented in the study are included in the article, further inquiries can be directed to the corresponding author.Funding
This research received no external funding.
Keywords
- finite element analysis
- incompressible Navier–Stokes equations
- partial differential equations
- tensor decompositions
- tensor trains
ASJC Scopus subject areas
- Computer Science (miscellaneous)
- General Mathematics
- Engineering (miscellaneous)