2 papers
math.NA2020
Rank-adaptive tensor methods for high-dimensional nonlinear PDEs
Alec Dektor, Abram Rodgers, Daniele Venturi
We present a new rank-adaptive tensor method to compute the numerical solution of high-dimensional nonlinear PDEs. The method combines functional tensor train (FTT) series expansio…
math.NA2019
Stability analysis of hierarchical tensor methods for time-dependent PDEs
Abram Rodgers, Daniele Venturi
In this paper we address the question of whether it is possible to integrate time-dependent high-dimensional PDEs with hierarchical tensor methods and explicit time stepping scheme…