5 research outputs found
Efficient GPU implementation of a Boltzmann‑Schrödinger‑Poisson solver for the simulation of nanoscale DG MOSFETs
81–102, 2019) describes an efficient and accurate solver for nanoscale DG MOSFETs
through a deterministic Boltzmann-Schrödinger-Poisson model with seven
electron–phonon scattering mechanisms on a hybrid parallel CPU/GPU platform.
The transport computational phase, i.e. the time integration of the Boltzmann equations,
was ported to the GPU using CUDA extensions, but the computation of the
system’s eigenstates, i.e. the solution of the Schrödinger-Poisson block, was parallelized
only using OpenMP due to its complexity. This work fills the gap by describing
a port to GPU for the solver of the Schrödinger-Poisson block. This new proposal
implements on GPU a Scheduled Relaxation Jacobi method to solve the sparse linear
systems which arise in the 2D Poisson equation. The 1D Schrödinger equation
is solved on GPU by adapting a multi-section iteration and the Newton-Raphson
algorithm to approximate the energy levels, and the Inverse Power Iterative Method
is used to approximate the wave vectors. We want to stress that this solver for the
Schrödinger-Poisson block can be thought as a module independent of the transport
phase (Boltzmann) and can be used for solvers using different levels of description
for the electrons; therefore, it is of particular interest because it can be adapted to
other macroscopic, hence faster, solvers for confined devices exploited at industrial
level.Project PID2020-117846GB-I00 funded by the Spanish Ministerio de Ciencia
e InnovaciónProject A-TIC-344-UGR20 funded by European
Regional Development Fund
Fluid models of mixed quantum-classical dynamics
Several efforts in nonadiabatic molecular dynamics are based on Madelung's
hydrodynamic description of nuclear motion, while the electronic component is
treated as a finite-dimensional quantum system. As the quantum potential in
Madelung hydrodynamics leads to severe challenges, one often seeks to neglect
its contribution thereby approximating nuclear motion as classical. Then, the
resulting model couples classical hydrodynamics for the nuclei to the quantum
motion of the electronic component. Such mixed quantum-classical fluid models
have also appeared in solvation dynamics to describe the coupling between
liquid solvents and the quantum solute molecule. While these approaches
represent a promising direction, their mathematical structure requires a
certain care. In some cases, challenging second-order gradients make these
equations hardly tractable. In other cases, these models are based on
phase-space formulations that suffer from well-known consistency issues. Here,
we present new quantum-classical fluid system that resolves these issues.
Unlike common approaches, the current system is obtained by applying the fluid
closure at the level of the action principle of the original phase-space model,
thereby inheriting variational and Hamiltonian structures, and ensuring
energy/momentum balance. After discussing some of its structural properties and
dynamical invariants, we illustrate the proposed fluid model in the case of
pure-dephasing systems. We conclude with a presentation of some invariant
planar models.Comment: 28 pages, including appendices. No figure
Generalized averaged Gaussian quadrature and applications
A simple numerical method for constructing the optimal generalized averaged Gaussian quadrature formulas will be presented. These formulas exist in many cases in which real positive GaussKronrod formulas do not exist, and can be used as an adequate alternative in order to estimate the error of a Gaussian rule. We also investigate the conditions under which the optimal averaged Gaussian quadrature formulas and their truncated variants are internal
MS FT-2-2 7 Orthogonal polynomials and quadrature: Theory, computation, and applications
Quadrature rules find many applications in science and engineering. Their analysis is a classical area of applied mathematics and continues to attract considerable attention. This seminar brings together speakers with expertise in a large variety of quadrature rules. It is the aim of the seminar to provide an overview of recent developments in the analysis of quadrature rules. The computation of error estimates and novel applications also are described