相关论文: Multigrid Methods in Electronic Structure Calculat…

An algorithm for simulating self-gravitating cosmological astrophysical fluids is presented. The advantages include a large dynamic range, parallelizability, high resolution per grid element and fast execution speed. The code is based on a…

Many problems in fluid modelling require the efficient solution of highly anisotropic elliptic partial differential equations (PDEs) in "flat" domains. For example, in numerical weather- and climate-prediction an elliptic PDE for the…

We solve Poisson's equation using new multigrid algorithms that converge rapidly. The novel feature of the 2D and 3D algorithms are the use of extra diagonal grids in the multigrid hierarchy for a much richer and effective communication…

The goal of this primer is to provide a relatively short exposition of the basics of multigrid methods, simplified by focusing on fundamental concepts in a variational setting. This is done by way of a quadratic energy minimization…

The method of McCurdy, Baertschy, and Rescigno, J. Phys. B, 37, R137 (2004) is generalized to obtain a straightforward, surprisingly accurate, and scalable numerical representation for calculating the electronic wave functions of molecules.…

We have developed an efficient computational scheme utilizing the real-space finite-difference formalism and the projector augmented-wave (PAW) method to perform precise first-principles electronic-structure simulations based on the density…

High precision atomic data is indispensable for experiments involving studies of fundamental interactions, astrophysics, atomic clocks, plasma science, and others. We develop new parallel atomic structure codes and explore the difficulties…

The ground state energy of a many-electron system can be approximated by an variational approach in which the total energy of the system is minimized with respect to one and two-body reduced density matrices (RDM) instead of many-electron…

A novel low complexity method to perform self-consistent electronic-structure calculations using the Kohn-Sham formalism of density functional theory is presented. Localization constraints are neither imposed nor required thereby allowing…

Multiple time-scale algorithms exploit the natural separation of time-scales in chemical systems to greatly accelerate the efficiency of molecular dynamics simulations. Although the utility of these methods in systems where the interactions…

Dielectric microstructures have generated much interest in recent years as a means of accelerating charged particles when powered by solid state lasers. The acceleration gradient (or particle energy gain per unit length) is an important…

Due to the wide separation of time scales in geophysical fluid dynamics, semi-implicit time integrators are commonly used in operational atmospheric forecast models. They guarantee the stable treatment of fast (acoustic and gravity) waves,…

Many problems in computational science and engineering involve partial differential equations and thus require the numerical solution of large, sparse (non)linear systems of equations. Multigrid is known to be one of the most efficient…

In this paper, we study a conjugate gradient method for electronic structure calculations. We propose a Hessian based step size strategy, which together with three orthogonality approaches yields three algorithms for computing the ground…

In this work, we propose an efficient and robust multigrid method for solving the time-fractional heat equation. Due to the nonlocal property of fractional differential operators, numerical methods usually generate systems of equations for…

Ab initio simulations are capable of providing detailed information of material behavior at the nanoscale. Simulating experimentally relevant situations is, however, often computationally intense. Using hybrid approaches between ab initio…

The Kohn-Sham scheme of density functional theory is one of the most widely used methods to solve electronic structure problems for a vast variety of atomistic systems across different scientific fields. While the method is fast relative to…

Multiresolution analysis of electronic structure affords the opportunity to capture the full physics of atomic cores in a systematically improvable manner. Applying new techniques, we demonstrate for the first time that multiresolution…

The novel contribution of this paper relies in the proposal of a fully implicit numerical method designed for nonlinear degenerate parabolic equations, in its convergence/stability analysis, and in the study of the related computational…

A challenge for molecular quantum dynamics (QD) calculations is the curse of dimensionality with respect to the nuclear degrees of freedom. A common approach that works especially well for fast reactive processes is to reduce the…