Accelerating scientific codes by performance and accuracy modeling

Scientific software is often driven by multiple parameters that affect both accuracy and performance. Since finding the optimal configuration of these parameters is a highly complex task, it extremely common that the software is used suboptimally. In a typical scenario, accuracy requirements are imposed, and attained through suboptimal performance. In this paper, we present a methodology for the automatic selection of parameters for simulation codes, and a corresponding prototype tool. To be amenable to our methodology, the target code must expose the parameters affecting accuracy and performance, and there must be formulas available for error bounds and computational complexity of the underlying methods. As a case study, we consider the particle-particle particle-mesh method (PPPM) from the LAMMPS suite for molecular dynamics, and use our tool to identify configurations of the input parameters that achieve a given accuracy in the shortest execution time. When compared with the configurations suggested by expert users, the parameters selected by our tool yield reductions in the time-to-solution ranging between 10% and 60%. In other words, for the typical scenario where a fixed number of core-hours are granted and simulations of a fixed number of timesteps are to be run, usage of our tool may allow up to twice as many simulations. While we develop our ideas using LAMMPS as computational framework and use the PPPM method for dispersion as case study, the methodology is general and valid for a range of software tools and methods

Multiple Staggered Mesh Ewald: Boosting the Accuracy of the Smooth Particle Mesh Ewald Method

The smooth particle mesh Ewald (SPME) method is the standard method for computing the electrostatic interactions in the molecular simulations. In this work, the multiple staggered mesh Ewald (MSME) method is proposed to boost the accuracy of the SPME method. Unlike the SPME that achieves higher accuracy by refining the mesh, the MSME improves the accuracy by averaging the standard SPME forces computed on, e.g. $M$, staggered meshes. We prove, from theoretical perspective, that the MSME is as accurate as the SPME, but uses $M^2$ times less mesh points in a certain parameter range. In the complementary parameter range, the MSME is as accurate as the SPME with twice of the interpolation order. The theoretical conclusions are numerically validated both by a uniform and uncorrelated charge system, and by a three-point-charge water system that is widely used as solvent for the bio-macromolecules

Tackling Exascale Software Challenges in Molecular Dynamics Simulations with GROMACS

GROMACS is a widely used package for biomolecular simulation, and over the last two decades it has evolved from small-scale efficiency to advanced heterogeneous acceleration and multi-level parallelism targeting some of the largest supercomputers in the world. Here, we describe some of the ways we have been able to realize this through the use of parallelization on all levels, combined with a constant focus on absolute performance. Release 4.6 of GROMACS uses SIMD acceleration on a wide range of architectures, GPU offloading acceleration, and both OpenMP and MPI parallelism within and between nodes, respectively. The recent work on acceleration made it necessary to revisit the fundamental algorithms of molecular simulation, including the concept of neighborsearching, and we discuss the present and future challenges we see for exascale simulation - in particular a very fine-grained task parallelism. We also discuss the software management, code peer review and continuous integration testing required for a project of this complexity.Comment: EASC 2014 conference proceedin

Fast and spectrally accurate summation of 2-periodic Stokes potentials

We derive a Ewald decomposition for the Stokeslet in planar periodicity and a novel PME-type O(N log N) method for the fast evaluation of the resulting sums. The decomposition is the natural 2P counterpart to the classical 3P decomposition by Hasimoto, and is given in an explicit form not found in the literature. Truncation error estimates are provided to aid in selecting parameters. The fast, PME-type, method appears to be the first fast method for computing Stokeslet Ewald sums in planar periodicity, and has three attractive properties: it is spectrally accurate; it uses the minimal amount of memory that a gridded Ewald method can use; and provides clarity regarding numerical errors and how to choose parameters. Analytical and numerical results are give to support this. We explore the practicalities of the proposed method, and survey the computational issues involved in applying it to 2-periodic boundary integral Stokes problems

Particle-Particle, Particle-Scaling function (P3S) 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. An MPI parallelised version of the code can be downloaded under the GNU General Public License from the website of our group.Comment: 19 pages, 11 figures, submitted to: Journal of Chemical Physic