This work develops tensor-train (TT) formulations for solving large-scale three-dimensional linear elasticity problems discretized by isogeometric analysis. By exploiting the tensor-product structure of the basis functions and the low-rank structure of geometry-dependent coefficient fields, the stiffness operator, mass operator, force vector, and displacement solution are represented in TT format. Two solution strategies are investigated: a block-operator formulation, in which the coupled elasticity operator is stored as separated TT blocks, and a single-operator formulation, in which the full coupled system is stored as one monolithic TT operator. A matrix-free three-field TT conjugate-gradient solver is introduced for the block formulation, while AMEn is used for the single-operator formulation. Numerical examples demonstrate substantial compression of both operators and solutions compared with conventional sparse full-grid representations, showing that TT-based formulations provide an efficient and scalable approach for large-scale three-dimensional elasticity simulations.
A principled fiber-dependency elimination framework is introduced that resolves this obstacle by expressing neighboring fibers as linear combinations of the cross-selected fibers through cross interpolation identities, which produces a closed collocation system while preserving the principal advantages of TT-cross meth...
Behzad Ghahremani, H. Babaee· arXiv.org· 1 citation
It is proven that all limit points of the iterative sequences generated by the method satisfy the KKT conditions for the underlying optimization problem, and under certain assumptions, it is proved that this method achieves Q-linear convergence.
Mao-Lin Liang, Li-Fang Dai, Rui-Juan Zhao et al.· Journal of Scientific Comput...· 0 citations
Numerical experiments show that the projection-based low-rank approach for assembling the mass and stiffness tensors of orientation-preserving tensor-product B-spline geometries is competitive with full assembly and with the interpolation-based low-rank method, and that it applies in two situations in which interpolati...
This work develops TTD- and HTD-based formulations for the T-product and its associated key algebra by operating directly on the factor matrices or tensors of the decompositions of the decompositions.
Yi-Dan Mei, Sheng-Han Mei, Zi-Qin He et al.· 0 citations
Plasolver, a physics-informed neural operator framework that combines the efficiency of operator learning with the accuracy and robustness of classical numerical solvers, provides an efficient, accurate, and discretization-invariant computational framework for nonlinear, path-dependent elastoplastic problems.
Yi-Zheng Wang, M. Eshaghi, Hua-Dong Zhang et al.· 0 citations
Tensor networks are powerful formats for compressing large-scale data. However, their application to general data processing has been limited by the difficulty of performing nonlinear operations. Here, we introduce iterative tensor network transformations (ITNTs), a general algorithmic framework for the element-wise ev...
Xiao Wang, Tomohiro Hashizume, Pia Siegl et al.· 2 citations
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