Comput Visual Sci (2008) 11:115–122 DOI 10.1007/s00791-007-0062-0 REGULAR ARTICLE A parallel multigrid accelerated Poisson solver for ab initio molecular dynamics applications H. Köstler · R. Schmid · U. Rüde · Ch. Scheit Received: 29 December 2005 / Accepted: 14 June 2006 / Published online: 6 February 2007 © Springer-Verlag 2007 Abstract In this paper we present an application for a parallel multigrid solver in 3D to solve the Coulomb problem for the charge self interaction in a quantum- chemical program used to perform ab initio molecular dynamics. Techniques such as Mehrstellendiscretization and τ -extrapolation are used to improve the discretiza- tion error. The results show that the expected conver- gence rates and parallel performance of the multigrid solver are achieved. Within the applied Carr–Parrinello Molecular Dynamics scheme the quality of the solution also determines the accuracy in energy conservation. All forms of discretization employed lead to energy con- serving dynamics. In order to test the applicability of our code to larger systems in a massively parallel envi- ronment, we investigated a 256 atom periodic supercell of bulk gallium nitride. 1 Introduction The development of efficient tools to calculate the elec- tronic structure of molecules as well as extended systems Communicated by P. Wesseling. R. Schmid Ruhr-University Bochum, 44780 Bochum, Germany e-mail: rochus.schmid@rub.de H. Köstler (B ) · U. Rüde · Ch. Scheit University of Erlangen-Nuremberg, 91058 Erlangen, Germany e-mail: Harald.Koestler@informatik.uni-erlangen.de U. Rüde e-mail: Ulrich.Ruede@informatik.uni-erlangen.de Ch. Scheit e-mail: cscheit@informatik.uni-erlangen.de on an ab initio level greatly enlarged the importance of theoretical simulation methods for fields like new materials research, catalysis or nanotechnology [8, 10]. The majority of modern computer codes for large scale systems are based on the expansion of electronic wave- functions and densities in terms of plane waves (PW). However, since some of the necessary integrals are eval- uated in Fourier space but others can only be calculated in real space (RS) the 3D-FFT is heavily used to trans- form back and forth. This leads to complications for the parallelization of the approach for massively paral- lel computer systems as the 3D-FFT involves a global communication step [34]. In addition, the intrinsic peri- odicity of PW limits the application to interesting sys- tems with reduced dimensionality as e.g. 2D periodic surfaces of high interest in various areas of research. As a consequence, more recently real space methods have been developed [7, 12, 14, 21, 26, 27, 37, 39–41], where all quantities are described on a real space mesh and FFT is no longer necessary, all communication operations are local, and arbitrary boundary conditions (as 2D peri- odicity) are simply realized. In the more traditional forms of electronic structure calculations with spheri- cal atom-centered basis functions for finite systems or PW based methods for periodic systems, which have originally been developed mostly within the theoretical chemistry and physics community, to some extent the knowledge of the solution has been used to make the calculation tractable. In contrast to that the real space approach is more similar to grid based methods used in many other fields of science like for example fluid dynamics or astronomy. An advantage is the simplicity of the algorithms. However, the knowledge and com- petence of the Computational Science community that has developed very efficient grid based methods to solve