Related papers: tRecX -- an environment for solving time-dependent…
The purpose of this document is to describe the solution and implementation of the time-independent and time-dependent Schr\"odinger using pseudospectral methods. Currently, the description is for single particle systems interacting with a…
Configuration-space matrix elements of N-body potentials arise naturally and ubiquitously in the Ritz-Galerkin solution of many-body quantum problems. For the common specialization of local, finite-range potentials, we develop the eXact…
Open Computing Language (OpenCL) is a parallel processing language that is ideally suited for running parallel algorithms on Graphical Processing Units (GPUs). In the present work we report on the development of a generic parallel…
We study low-rank tensor methods for the numerical solution of Schr\"odinger's equation with time-independent and explicitly time-dependent Hamiltonians, motivated by large-scale simulations of many-body quantum systems and quantum…
As a first approximation beyond linearity, the nonlinear Schr\"odinger equation (NLSE) reliably describes a broad class of physical systems. Though numerical solutions of this model are well-established, these methods can be computationally…
High-dimensional time series has diverse applications in econometrics and finance. Recent models for capturing temporal dependence have employed a bilinear representation for matrix time series, or the Tucker-decomposition based…
The Trotter-Suzuki approximation leads to an efficient algorithm for solving the time-dependent Schr\"odinger equation. Using existing highly optimized CPU and GPU kernels, we developed a distributed version of the algorithm that runs…
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 expansions, operator splitting time integration, and a new…
In this work, we introduce PHOENIX, a highly optimized explicit open-source solver for two-dimensional nonlinear Schr\"odinger equations with extensions. The nonlinear Schr\"odinger equation and its extensions (Gross-Pitaevskii equation)…
We present a unified hard-constraint framework for solving geometrically complex PDEs with neural networks, where the most commonly used Dirichlet, Neumann, and Robin boundary conditions (BCs) are considered. Specifically, we first…
Discrete Lossless Convexification (DLCvx) formulates a convex relaxation for a specific class of discrete-time non-convex optimal control problems. It establishes sufficient conditions under which the solution of the relaxed problem…
We consider tensors in the Hierarchical Tucker format and suppose the tensor data to be distributed among several compute nodes. We assume the compute nodes to be in a one-to-one correspondence with the nodes of the Hierarchical Tucker…
We introduce a general differentiable solver for time-dependent deformation problems with contact and friction. Our approach uses a finite element discretization with a high-order time integrator coupled with the recently proposed…
GRTresna is a multigrid solver designed to solve the constraint equations for the initial data required in numerical relativity simulations. In particular, it is focussed on scenarios with fundamental fields around black holes and…
Exponential time differencing methods is a power tool for high-performance numerical simulation of computationally challenging problems in condensed matter physics, fluid dynamics, chemical and biological physics, where mathematical models…
A numerical approach for solving evolutionary partial differential equations in two and three space dimensions on block-based adaptive grids is presented. The numerical discretization is based on high-order, central finite-differences and…
Developing parallel algorithms efficiently requires careful management of concurrency across diverse hardware architectures. C++ executors provide a standardized interface that simplifies the development process, allowing developers to…
The multiconfigurational time-dependent Hartree-Fock equations are discussed and solved for a one-dimensional model of the Helium atom. Results for the ground state energy and two-particle density as well as the absorption spectrum are…
In this paper, the trial function method is employed to find the exact solutions for high-order nonlinear Schr\"odinger equations with time-dependent coefficients. This system describes the propagation of ultrashort light pulses in…
This paper presents the SCvx algorithm, a successive convexification algorithm designed to solve non-convex constrained optimal control problems with global convergence and superlinear convergence-rate guarantees. The proposed algorithm can…