Related papers: Real-Space Mesh Techniques in Density Functional T…
We present a multigrid algorithm for self consistent solution of the Kohn-Sham equations in real space. The entire problem is discretized on a real space mesh with a high order finite difference representation. The resulting self consistent…
We present a set of efficient techniques in first-principles electronic-structure calculations utilizing the real-space finite-difference method. These techniques greatly reduce the overhead for performing integrals that involve…
Optimal exploitation of supercomputing resources for the evaluation of electrostatic forces remains a challenge in molecular dynamics simulations of very large systems. The most efficient methods are currently based on particle-mesh Ewald…
Iterative multiscale methods for electronic structure calculations offer several advantages for large-scale problems. Here we examine a nonlinear full approximation scheme (FAS) multigrid method for solving fixed potential and…
A new method of solution to the local spin density approximation to the electronic Schr\"{o}dinger equation is presented. The method is based on an efficient, parallel, adaptive multigrid eigenvalue solver. It is shown that adaptivity is…
A type of parallel augmented subspace scheme for eigenvalue problems is proposed by using coarse space in the multigrid method. With the help of coarse space in multigrid method, solving the eigenvalue problem in the finest space is…
Recent work on octree-based finite-element systems has developed a multigrid solver for Poisson equations on meshes. While the idea of defining a regularly indexed function space has been successfully used in a number of applications, it…
Developments in dynamical systems theory provides new support for the macroscale modelling of pdes and other microscale systems such as Lattice Boltzmann, Monte Carlo or Molecular Dynamics simulators. By systematically resolving subgrid…
We present a real-space adaptive-coordinate method, which combines the advantages of the finite-difference approach with the accuracy and flexibility of the adaptive coordinate method. The discretized Kohn-Sham equations are written in…
We describe a set of techniques for performing large scale ab initio calculations using multigrid accelerations and a real-space grid as a basis. The multigrid methods provide effective convergence acceleration and preconditioning on all…
To improve the computational efficiencies of the real-space orbital-free density functional theory, this work develops a new single-grid solver by directly providing the closed-form solution to the inner iteration and using an improved…
Large-scale eigenvalue problems arise in various fields of science and engineering and demand computationally efficient solutions. In this study, we investigate the subspace approximation for parametric linear eigenvalue problems, aiming to…
Discretizing an analytic function on a uniform real-space grid is often done via a straightforward collocation method. This is ubiquitous in all areas of computational physics and quantum chemistry. An example in Density Functional Theory…
Real-space grids are a powerful alternative for the simulation of electronic systems. One of the main advantages of the approach is the flexibility and simplicity of working directly in real space where the different fields are discretized…
In order to reduce the computational cost of the simulation of electromagnetic responses in geophysical settings that involve highly heterogeneous media, we develop a multiscale finite volume method with oversampling for the quasi-static…
We develop a new spatial semidiscrete multiscale method based upon the edge multiscale methods to solve semilinear parabolic problems with heterogeneous coefficients and smooth initial data. This method allows for a cheap spatial…
A numerical method is presented for first-principle simulations of charged colloidal dispersions in electrolyte solutions. Utilizing a smoothed profile for colloid-solvent boundaries, efficient mesoscopic simulations are enabled for…
Simulation in media with multiple continua where each continuum interacts with every other is often challenging due to multiple scales and high contrast. One needs some types of model reduction. One of the approaches is multi-continuum…
Starting from the observation that one of the most successful methods for solving the Kohn-Sham equations for periodic systems -- the plane-wave method -- is a spectral method based on eigenfunction expansion, we formulate a spectral method…
A grid-based real-space implementation of the Projector Augmented Wave (PAW) method of P. E. Blochl [Phys. Rev. B 50, 17953 (1994)] for Density Functional Theory (DFT) calculations is presented. The use of uniform 3D real-space grids for…