Optimization and Parallelization of a force field for silicon using OpenMP

The force field by Lenosky and coworkers is the latest force field for silicon which is one of the most studied materials. It has turned out to be highly accurate in a large range of test cases. The optimization and parallelization of this force field using OpenMp and Fortan90 is described here. The optimized program allows us to handle a very large number of silicon atoms in large scale simulations. Since all the parallelization is hidden in a single subroutine that returns the total energies and forces, this subroutine can be called from within a serial program in an user friendly way.Comment: The program can be obtained upon request from the author ([email protected]

Finite-temperature evaluation of the Fermi density operator

A rational expansion of the Fermi density operator is proposed. This approach allows to calculate efficiently physical properties of fermionic systems at finite temperatures without solving an eigenvalue problem. Using N evaluations of the Green's function, the Fermi density operator can be approximated, subject to a given precision, in the energy interval from -A to infinity with A proportional to N. The presented method may become especially useful for electronic structure calculations involving the calculation of charge densities.Comment: 6 pages, 4 Postscript figures, submitted to J. Comp. Phy

The solution of multi-scale partial differential equations using wavelets

Wavelets are a powerful new mathematical tool which offers the possibility to treat in a natural way quantities characterized by several length scales. In this article we will show how wavelets can be used to solve partial differential equations which exhibit widely varying length scales and which are therefore hardly accessible by other numerical methods. As a benchmark calculation we solve Poisson's equation for a 3-dimensional Uranium dimer. The length scales of the charge distribution vary by 4 orders of magnitude in this case. Using lifted interpolating wavelets the number of iterations is independent of the maximal resolution and the computational effort therefore scales strictly linearly with respect to the size of the system

Density Functional Theory calculation on many-cores hybrid CPU-GPU architectures

The implementation of a full electronic structure calculation code on a hybrid parallel architecture with Graphic Processing Units (GPU) is presented. The code which is on the basis of our implementation is a GNU-GPL code based on Daubechies wavelets. It shows very good performances, systematic convergence properties and an excellent efficiency on parallel computers. Our GPU-based acceleration fully preserves all these properties. In particular, the code is able to run on many cores which may or may not have a GPU associated. It is thus able to run on parallel and massive parallel hybrid environment, also with a non-homogeneous ratio CPU/GPU. With double precision calculations, we may achieve considerable speedup, between a factor of 20 for some operations and a factor of 6 for the whole DFT code.Comment: 14 pages, 8 figure

A Customized 3D GPU Poisson Solver for Free Boundary Conditions

A 3-dimensional GPU Poisson solver is developed for all possible combinations of free and periodic boundary conditions (BCs) along the three directions. It is benchmarked for various grid sizes and different BCs and a significant performance gain is observed for problems including one or more free BCs. The GPU Poisson solver is also benchmarked against two different CPU implementations of the same method and a significant amount of acceleration of the computation is observed with the GPU version.Comment: 10 pages, 5 figure

Efficient and accurate three dimensional Poisson solver for surface problems

We present a method that gives highly accurate electrostatic potentials for systems where we have periodic boundary conditions in two spatial directions but free boundary conditions in the third direction. These boundary conditions are needed for all kind of surface problems. Our method has an O(N log N) computational cost, where N is the number of grid points, with a very small prefactor. This Poisson solver is primarily intended for real space methods where the charge density and the potential are given on a uniform grid.Comment: 6 pages, 2 figure

An efficient numerical quadrature for the calculation of the potential energy of wavefunctions expressed in the Daubechies wavelet basis

An efficient numerical quadrature is proposed for the approximate calculation of the potential energy in the context of pseudo potential electronic structure calculations with Daubechies wavelet and scaling function basis sets. Our quadrature is also applicable in the case of adaptive spatial resolution. Our theoretical error estimates are confirmed by numerical test calculations of the ground state energy and wave function of the harmonic oscillator in one dimension with and without adaptive resolution. As a byproduct we derive a filter, which, upon application on the scaling function coefficients of a smooth function, renders the approximate grid values of this function. This also allows for a fast calculation of the charge density from the wave function.Comment: 35 pages, 9 figures. Submitted to: Journal of Computational Physic

Global minimum determination of the Born-Oppenheimer surface within density functional theory

We present a novel method, which we call dual minima hopping method (DMHM), that allows us to find the global minimum of the potential energy surface (PES) within density functional theory for systems where a fast but less accurate calculation of the PES is possible. This method can rapidly find the ground state configuration of clusters and other complex systems with present day computer power by performing a systematic search. We apply the new method to silicon clusters. Even though these systems have already been extensively studied by other methods, we find new configurations that are lower in energy than the previously found.Comment: 4 pages, 3 figures, minor changes, more structures are presented no