A tensor train-based isogeometric solver for large-scale 3D poisson problems

Tran, Quoc Thai; Truong, Duc P.; Rasmussen, Kim Orskov; Alexandrov, Boian

doi:10.1016/j.cma.2026.118802

A tensor train-based isogeometric solver for large-scale 3D poisson problems

Journal Article · Mon Feb 16 00:00:00 EST 2026 · Computer Methods in Applied Mechanics and Engineering

DOI:https://doi.org/10.1016/j.cma.2026.118802· OSTI ID:3019466

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Los Alamos National Laboratory (LANL), Los Alamos, NM (United States)

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.

View Accepted Manuscript (DOE)

Research Organization:: Los Alamos National Laboratory (LANL), Los Alamos, NM (United States)

Sponsoring Organization:: USDOE Laboratory Directed Research and Development (LDRD) Program; USDOE National Nuclear Security Administration (NNSA)

Grant/Contract Number:: 89233218CNA000001

Other Award/Contract Number:: 20230067DR
20250893ER

OSTI ID:: 3019466

Report Number(s):: LA-UR--25-29276; 10.1016/j.cma.2026.118802

Journal Information:: Computer Methods in Applied Mechanics and Engineering, Journal Name: Computer Methods in Applied Mechanics and Engineering Vol. 453; ISSN 0045-7825

Publisher:: ElsevierCopyright Statement

Country of Publication:: United States

Language:: English

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