A dynamic subspace method parameterizes low-dimensional bases as geodesic paths on the Grassmannian to track evolving physics in nonlinear systems, achieving higher accuracy than static approximations at the same rank.
Dynamical Low-Rank Approximation
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Combines Operator Fourier Transform with low-rank Cross-DEIM to accelerate 2D Helmholtz equation solutions via pseudo-time Schrödinger integrals.
The paper investigates the effects of time integrator selection, numerical dissipation, and problem representation on the efficiency and stability of quantized tensor train simulations for advection-dominated test problems.
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A Dynamic Subspace Approach for Low-rank Approximation of Large-scale Nonlinear Systems
A dynamic subspace method parameterizes low-dimensional bases as geodesic paths on the Grassmannian to track evolving physics in nonlinear systems, achieving higher accuracy than static approximations at the same rank.
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Low-Rank Acceleration of the Operator Fourier Transform
Combines Operator Fourier Transform with low-rank Cross-DEIM to accelerate 2D Helmholtz equation solutions via pseudo-time Schrödinger integrals.