Biomolecular electrostatics using a fast multipole BEM on up to 512 GPUs and a billion unknowns

Rio Yokota, Jaydeep P. Bardhan, Matthew G. Knepley, L. A. Barba, Tsuyoshi Hamada
Department of Mechanical Engineering, Boston University, Boston MA 02215
arXiv:1007.4591v3 [cs.CE] (10 Feb 2011)


   author={Yokota}, R. and {Bardhan}, J.~P. and {Knepley}, M.~G. and {Barba}, L.~A. and {Hamada}, T.},

   title={“{Biomolecular electrostatics using a fast multipole BEM on up to 512 GPUs and a billion unknowns}”},

   journal={ArXiv e-prints},




   keywords={Computer Science – Computational Engineering, Finance, and Science, Physics – Chemical Physics, Physics – Computational Physics},




   adsnote={Provided by the SAO/NASA Astrophysics Data System}


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We present teraflop-scale calculations of biomolecular electrostatics enabled by the combination of algorithmic and hardware acceleration. The algorithmic acceleration is achieved with the fast multipole method (FMM) in conjunction with a boundary element method (BEM) formulation of the continuum electrostatic model, as well as the BIBEE approximation to BEM. The hardware acceleration is achieved through graphics processors, GPUs. We demonstrate the power of our algorithms and software for the calculation of the electrostatic interactions between biological molecules in solution. The applications demonstrated include the electrostatics of protein–drug binding and several multi-million atom systems consisting of hundreds to thousands of copies of lysozyme molecules. The parallel scalability of the software was studied in a cluster at the Nagasaki Advanced Computing Center, using 128 nodes, each with 4 GPUs. Delicate tuning has resulted in strong scaling with parallel efficiency of 0.8 for 256 and 0.5 for 512 GPUs. The largest application run, with over 20 million atoms and one billion unknowns, required only one minute on 512 GPUs. We are currently adapting our BEM software to solve the linearized Poisson-Boltzmann equation for dilute ionic solutions, and it is also designed to be flexible enough to be extended for a variety of integral equation problems, ranging from Poisson problems to Helmholtz problems in electromagnetics and acoustics to high Reynolds number flow.
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