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A tensor train-based isogeometric solver for large-scale 3D poisson problems
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DOI：10.1016/j.cma.2026.118802.png)
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Abstract
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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.
Keywords:
Tensor train
Poisson equation
Isogeometric analysis
Tensor-product spline grids
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