2 papers
math.NA2025
Low-rank cross approximation of function-valued tensors for reduced-order modeling of parametric PDEs
Stanislav Budzinskiy, Vladimir Kazeev, Maxim Olshanskii
The paper considers function-valued tensors, viewed as multidimensional arrays with entries in an abstract Hilbert space. Despite the absence of the algebraic structure of a field,…
math.NA2024
Symplectic QTT-FEM solution of the one-dimensional acoustic wave equation in the time domain
Sara Fraschini, Vladimir Kazeev, Ilaria Perugia
Structured Finite Element Methods (FEMs) based on low-rank approximation in the form of the so-called Quantized Tensor Train (QTT) decomposition (QTT-FEM) have been proposed and ex…