Accelerating Sparse Arithmetic in the Context of Newton’s Method for Small 
Molecules with Bond Constraints

Mikkelsen, Carl Christian Kjelgaard; Alastruey-Benedé, Jesús; Ibáñez-Marín, Pablo; Risueño, Pablo García

doi:10.1007/978-3-319-32149-3_16

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Accelerating Sparse Arithmetic in the Context of Newton’s Method for Small Molecules with Bond Constraints

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Risueño, Pablo García
Theory, Fritz Haber Institute, Max Planck Society;
Institut für Physik, Humboldt Universität zu Berlin;
Instituto de Biocomputación y Física de Sistemas Complejos;

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Citation

Mikkelsen, C. C. K., Alastruey-Benedé, J., Ibáñez-Marín, P., & Risueño, P. G. (2016). Accelerating Sparse Arithmetic in the Context of Newton’s Method for Small Molecules with Bond Constraints. In R. Wyrzykowski, E. Deelman, J. Dongarra, K. Karczewski, J. Kitowski, & K. Wiatr (Eds.), Parallel Processing and Applied Mathematics (pp. 160-171). Berlin: Springer.

Cite as: https://hdl.handle.net/11858/00-001M-0000-002A-C4F6-9

Abstract

Molecular dynamics is used to study the time evolution of systems of atoms. It is common to constrain bond lengths in order to increase the time step of the simulation. Here we accelerate Newton’s method for solving the constraint equations for a system consisting of many identical small molecules. Starting with a modular and generic base code using a sequential data layout, we apply three different optimization techniques. The compiled code approach is used to generate subroutines equivalent to a single step of Newton’s method for a user specified molecule. Differing from the generic subroutines, these specific routines contain no loops and no indirect addressing. Interleaving the data describing different molecules generates vectorizable loops. Finally, we apply task fusion. The simultaneous application of all three techniques increases the speed of the base code by a factor of 15 for single precision calculations.