13 citations · 15 across the 4 of their papers we have counts for
5 papers
Tensor approximation of functional differential equations
Abram Rodgers, Daniele Venturi
Functional Differential Equations (FDEs) play a fundamental role in many areas of mathematical physics, including fluid dynamics (Hopf characteristic functional equation), quantum…
Implicit integration of nonlinear evolution equations on tensor manifolds
Abram Rodgers, Daniele Venturi
Explicit step-truncation tensor methods have recently proven successful in integrating initial value problems for high-dimensional partial differential equations (PDEs). However, t…
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…
Adaptive integration of nonlinear evolution equations on tensor manifolds
Abram Rodgers, Alec Dektor, Daniele Venturi
We develop new adaptive algorithms for temporal integration of nonlinear evolution equations on tensor manifolds. These algorithms, which we call step-truncation methods, are based…
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…