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DOE OSTI · 3019466

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

Tran, Quoc Thai [Los Alamos National Laboratory (LANL), Los Alamos, NM (United States)] (ORCID:0000000186806395)·Truong, Duc P. [Los Alamos National Laboratory (LANL), Los Alamos, NM (United States)] (ORCID:0000000298063274)·Rasmussen, Kim Orskov [Los Alamos National Laboratory (LANL), Los Alamos, NM (United States)] (ORCID:0000000240294723)·Alexandrov, Boian [Los Alamos National Laboratory (LANL), Los Alamos, NM (United States)] (ORCID:0000000186364603)
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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.

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97 MATHEMATICS AND COMPUTINGIsogeometric analysisPoisson equationTensor trainTensor-product spline grids

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Tran, Quoc Thai [Los Alamos National Laboratory (LANL), Los Alamos, NM (United States)] (ORCID:0000000186806395), Truong, Duc P. [Los Alamos National Laboratory (LANL), Los Alamos, NM (United States)] (ORCID:0000000298063274), Rasmussen, Kim Orskov [Los Alamos National Laboratory (LANL), Los Alamos, NM (United States)] (ORCID:0000000240294723), Alexandrov, Boian [Los Alamos National Laboratory (LANL), Los Alamos, NM (United States)] (ORCID:0000000186364603). 2026-02-16. A tensor train-based isogeometric solver for large-scale 3D poisson problems. https://doi.org/10.1016/j.cma.2026.118802

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