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math.NA2026
A Polynomial-Scaling PDE Solver with Entanglement-Basis Tensor Networks
Abhijatmedhi Chotrattanapituk, Michael J. Landry, Chu-Liang Fu +1
We develop a finite element method (FEM) for partial differential equation (PDE) solver based on the entanglement-basis representation introduced in our companion work. By lifting…
math.NA2026
Tensor-Network Finite Elements for Analytic Operator Equations
Abhijatmedhi Chotrattanapituk, Michael J. Landry, Chu-Liang Fu +1
Operator equations (OEs) underpin quantitative modeling across science and engineering. Finite-element (FE) methods discretize continuous OEs into finite-dimensional algebraic syst…
cond-mat.mtrl-sci2026
Quantum Theory of Functionally Graded Materials
Michael J. Landry, Ryotaro Okabe, Chuliang Fu +1
Functionally graded materials (FGMs) are composites whose composition or microstructure varies continuously in space, producing position-dependent mechanical and functional propert…