A tensor train-based isogeometric solver for large-scale 3D poisson problems
Abstract
We introduce a three-dimensional (3D), fully tensor train (TT) assembled isogeometric analysis (IGA) framework, TT-IGA, for solving partial differential equations (PDEs). Our method reformulates IGA discrete operators into TT format, enabling efficient compression and computation. Geometry evaluations use the original NURBS description at sampling points and TT approximation is applied to geometry-derived coefficient fields and discrete operators. We demonstrate the effectiveness of the proposed TT-IGA framework on the three-dimensional Poisson equation, achieving substantial reductions in memory and computational cost without compromising solution quality.
Fields of Study & Subjects
Advanced Numerical Analysis Techniques
Polynomial and algebraic computation
Computational Geometry and Mesh Generation
Publication details
- Journal / source
- Computer Methods in Applied Mechanics and Engineering
- Publisher
- Elsevier BV
- Volume
- 453
- Pages
- 118802–118802
- Publication date
- 16 February 2026
- Language
- EN