Interlaced P3M algorithm with analytical and ik-differentiation.

The interlacing technique of Hockney and Eastwood is extended to the particle-particle, particle-mesh (P3M) algorithm with analytical and ik-differentiation that computes the approximate Coulomb forces between N point particles in a periodic box. Interlacing means that one makes two separate computations of the reciprocal-space Ewald force, using two grids shifted with respect to each other by half of the diagonal of the grid subcell, and then takes the average of the two forces. The resulting algorithms compare favorably against their own noninterlaced versions and against the interlaced smooth particle-mesh Ewald algorithm. In our tests, the accuracy of the interlaced P3M methods was usually more than an order of magnitude higher than that of the other particle-mesh algorithms with the same parameter values. This accuracy gain can be converted into a speedup if the parameters of the algorithm are changed. Interlacing allows one to increase the grid spacing by up to a factor of 2 while keeping the same accuracy. A priori error estimates for the new algorithms are constructed, and the removal of the spurious self-force term is discussed. The success of interlacing is shown to be due to the fact that it suppresses the aliasing effects in the forces. It should be easy to incorporate the interlaced P3M algorithms into an existing simulation package, since this only requires a minor modification of the particle-mesh Ewald part of the code.

Adsorption of small NaCl clusters on surfaces of silicon nanostructures.

We have studied possible adsorption geometries of neutral NaCl clusters on the disordered surface of a large silicon model tip used in non-contact atomic force microscopy. The minima hopping method was used to determine low energy model tip configurations as well as ground state geometries of isolated NaCl clusters. The combined system was treated with density functional theory. Alkali halides have proven to be strong structure seekers and tend to form highly stable ground state configurations whenever possible. The favored adsorption geometry for four Na and four Cl atoms was found to be an adsorption of four NaCl dimers due to the formation of Cl-Si bonds. However, for larger NaCl clusters, the increasing energy required to dissociate the cluster into NaCl dimers suggests that adsorption of whole clusters in their isolated ground state configuration is preferred.

Density functional theory calculation on many-cores hybrid central processing unit-graphic processing unit architectures.

We present the implementation of a full electronic structure calculation code on a hybrid parallel architecture with graphic processing units (GPUs). This implementation is performed on a free software code based on Daubechies wavelets. Such code 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, and thus on parallel and massive parallel hybrid machines. 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 density functional theory code.

Daubechies wavelets as a basis set for density functional pseudopotential calculations.

Daubechies wavelets are a powerful systematic basis set for electronic structure calculations because they are orthogonal and localized both in real and Fourier space. We describe in detail how this basis set can be used to obtain a highly efficient and accurate method for density functional electronic structure calculations. An implementation of this method is available in the ABINIT free software package. This code shows high systematic convergence properties, very good performances, and an excellent efficiency for parallel calculations.

Particle-particle, particle-scaling function algorithm for electrostatic problems in free boundary conditions.

An algorithm for fast calculation of the Coulombic forces and energies of point particles with free boundary conditions is proposed. Its calculation time scales as N log N for N particles. This novel method has lower crossover point with the full O(N(2)) direct summation than the fast multipole method. The forces obtained by our algorithm are analytical derivatives of the energy which guarantees energy conservation during a molecular dynamics simulation. Our algorithm is very simple. A version of the code parallelized with the Message Passing Interface can be downloaded under the GNU General Public License from the website of our group.

A particle-particle, particle-density algorithm for the calculation of electrostatic interactions of particles with slablike geometry.

We present a fast and accurate method to calculate the electrostatic energy and forces of interacting particles with the boundary conditions appropriate to surfaces, i.e., periodic in the two directions parallel to the surface and free in the perpendicular direction. In the spirit of the Ewald method, the problem is divided into a short range and a long range part. The charge density responsible for the long range part is represented by plane waves in the periodic directions and by finite elements in the nonperiodic direction. Our method has computational complexity of O(N(g) log(N(g))) with a very small prefactor, where N(g) is the number of grid points.

Efficient solution of Poisson's equation with free boundary conditions.

Interpolating scaling functions give a faithful representation of a localized charge distribution by its values on a grid. For such charge distributions, using a fast Fourier method, we obtain highly accurate electrostatic potentials for free boundary conditions at the cost of O(N log N) operations, where N is the number of grid points. Thus, with our approach, free boundary conditions are treated as efficiently as the periodic conditions via plane wave methods.