1 citations · 3 across the 11 of their papers we have counts for
11 papers
The low-rank tensor-train finite difference method for three-dimensional parabolic equations
Gianmarco Manzini, Tommaso Sorgente
This paper presents a numerical framework for the low-rank approximation of the solution to three-dimensional parabolic problems. The key contribution of this work is the tensoriza…
A Fast, Accurate and Oscillation-free Spectral Collocation Solver for High-dimensional Transport Problems
Nicola Cavallini, Gianmarco Manzini, Daniele Funaro +1
Transport phenomena-describing the movement of particles, energy, or other physical quantities-are fundamental in various scientific disciplines, including nuclear physics, plasma…
The Tensor-Train Stochastic Finite Volume Method for Uncertainty Quantification
Steven Walton, Svetlana Tokareva, Gianmarco Manzini
The stochastic finite volume method offers an efficient one-pass approach for assessing uncertainty in hyperbolic conservation laws. Still, it struggles with the curse of dimension…
Tensor Network Space-Time Spectral Collocation Method for Time Dependent Convection-Diffusion-Reaction Equations
Dibyendu Adak, Duc P. Truong, Gianmarco Manzini +2
Emerging tensor network techniques for solutions of Partial Differential Equations (PDEs), known for their ability to break the curse of dimensionality, deliver new mathematical me…
Tensor Networks for Solving Realistic Time-independent Boltzmann Neutron Transport Equation
Duc P. Truong, Mario I. Ortega, Ismael Boureima +3
Tensor network techniques, known for their low-rank approximation ability that breaks the curse of dimensionality, are emerging as a foundation of new mathematical methods for ultr…
A -conforming arbitrary-order two-dimensional virtual element method for the fourth-order phase-field equation
Dibyendu Adak, Gianmarco Manzini, Hashem M. Mourad +2
We present a two-dimensional conforming virtual element method for the fourth-order phase-field equation. Our proposed numerical approach to the solution of this high-order phase-f…