Related papers: Large Scale Electronic Structure Calculations with…

To numerically solve a generic elliptic equation on two-dimensional domains with rectangular Cartesian grids, we propose a cut-cell geometric multigrid method that features (1) general algorithmic steps that apply to two-dimensional…

We show how graph theory can be combined with quantum theory to calculate the electronic structure of large complex systems. The graph formalism is general and applicable to a broad range of electronic structure methods and materials,…

The geometric high-order regularization methods such as mean curvature and Gaussian curvature, have been intensively studied during the last decades due to their abilities in preserving geometric properties including image edges, corners,…

An approach is given for solving large linear systems that combines Krylov methods with use of two different grid levels. Eigenvectors are computed on the coarse grid and used to deflate eigenvalues on the fine grid. GMRES-type methods are…

The paper presents AMGCL -- an opensource C++ library implementing the algebraic multigrid method (AMG) for solution of large sparse linear systems of equations, usually arising from discretization of partial differential equations on an…

Laplacian matrices of graphs arise in large-scale computational applications such as machine learning; spectral clustering of images, genetic data and web pages; transportation network flows; electrical resistor circuits; and elliptic…

Methods exhibiting linear scaling with respect to the size of the system, so called O(N) methods, are an essential tool for the calculation of the electronic structure of large systems containing many atoms. They are based on algorithms…

We present an approach to solid-state electronic-structure calculations based on the finite-element method. In this method, the basis functions are strictly local, piecewise polynomials. Because the basis is composed of polynomials, the…

The computation of stationary distributions of Markov chains is an important task in the simulation of stochastic models. The linear systems arising in such applications involve non-symmetric M-matrices, making algebraic multigrid methods a…

We discuss our new implementation of the Real-space Electronic Structure method for studying the atomic and electronic structure of infinite periodic as well as finite systems, based on density functional theory. This improved version which…

The LDA+DMFT method is a very powerful tool for gaining insight into the physics of strongly correlated materials. It combines traditional ab-initio density-functional techniques with the dynamical mean-field theory. The core aspects of the…

A general real-space multigrid algorithm MIKA (Multigrid Instead of the K-spAce) for the self-consistent solution of the Kohn-Sham equations appearing in the state-of-the-art electronic-structure calculations is described. The most…

In this chapter we focus first on the theoretical methods and relevant computational approaches to calculate the electronic structure of atoms, molecules, and clusters containing heavy elements for which relativistic effects become…

Complex band structures (CBSs) are useful to characterize the static and dynamical electronic properties of materials. Despite the intensive developments, the first-principles calculation of CBS for over several hundred atoms is still…

While recent work towards the development of tight-binding and ab-initio algorithms has focused on molecular dynamics, Monte Carlo methods can often lead to better results with relatively little effort. We present here a multi-step Monte…

A recently developed density functional method, within Hohenberg-Kohn-Sham framework, is used for faithful description of atoms, molecules in Cartesian coordinate grid, by using an LCAO-MO ansatz. Classical Coulomb potential is obtained by…

3D non-LTE radiative transfer problems are computationally demanding, and this sets limits on the size of the problems that can be solved. So far Multilevel Accelerated Lambda Iteration (MALI) has been to the method of choice to perform…

We have developed an efficient and reliable methodology for crystal structure prediction, merging ab initio total-energy calculations and a specifically devised evolutionary algorithm. This method allows one to predict the most stable…

The multigrid methodology is reviewed. By integrating numerical processes at all scales of a problem, it seeks to perform various computational tasks at a cost that rises as slowly as possible as a function of $n$, the number of degrees of…

Evaluation of a wide variety of Feynman diagrams with multi-loop integrals and physical parameters and its comparison with high energy experiments are expected to investigate new physics beyond the Standard Model. We have been developing a…