24 citations · 55 across the 12 of their papers we have counts for
4 papers · 1 filter
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…
Dynamic tensor approximation of high-dimensional nonlinear PDEs
Alec Dektor, Daniele Venturi
We present a new method based on functional tensor decomposition and dynamic tensor approximation to compute the solution of a high-dimensional time-dependent nonlinear partial dif…
Spectral methods for nonlinear functionals and functional differential equations
Daniele Venturi, Alec Dektor
We present a rigorous convergence analysis for cylindrical approximations of nonlinear functionals, functional derivatives, and functional differential equations (FDEs). The purpos…