Electron Dynamics on Graphics Processing Units Xavier Andrade - PowerPoint PPT Presentation

Electron Dynamics on Graphics Processing Units Xavier Andrade Lawrence Livermore National Laboratory xavier@llnl.gov

simulation at the atomic scale predict and understand properties of materials

molecular dynamics: classical atoms connected by 'springs'

electron dynamics: simulate the time-evolution of electrons as quantum particles

interaction of lasers with matter

atomic collisions

stopping of fast particles in materials Work by A. Correa, Lawrence Livermore National Laboratory

conductivity in metals liquid aluminum

simulation of excited state of light harvesting complex II full tddft with 6075 atoms scaling to 300,000 cores J. Jornet-Somoza, J. Alberdi-Rodriguez, B. F. Milne, X. Andrade, M.A.L. Marques, F. Nogueira, M.J.T. Oliveira, J. J. P. Stewart and A. Rubio, PCCP 17 26599 (2015)

optical absorption J. Jornet-Somoza, J. Alberdi-Rodriguez, B. F. Milne, X. Andrade, M.A.L. Marques, F. Nogueira, M.J.T. Oliveira, J. J. P. Stewart and A. Rubio, PCCP 17 26599 (2015)

local multipole analysis stroma lumen chlorophyll a chlorophyll b J. Jornet-Somoza, J. Alberdi-Rodriguez, B. F. Milne, X. Andrade, M.A.L. Marques, F. Nogueira, M.J.T. Oliveira, J. J. P. Stewart and A. Rubio, PCCP 17 26599 (2015)

we can scale electron dynamics up to 1.6 million CPU cores qb@ll plane-wave code 8.8 petaflop/s (44% of peak) E. W. Draeger, X. Andrade, J.A. Gunnels, A. Bhatele, A. Schleife, A.A. Correa, "Massively parallel first-principles simulation of electron dynamics in materials", accepted to IDPDS 2016

implementing electron dynamics on gpus

the octopus code finite and periodic real-space pseudo-potential systems grids approximation X. Andrade et al, PCCP, 17 31371 (2015) http://tddft.org/programs/octopus/

real-time tddft equations i ∂ ∂ t ϕ j ( r , t ) = H ( t ) ϕ j ( r , t ) 2 � � n ( r , t ) = ∑ � ϕ j ( r , t ) � � � j 1

integration in time of tddft equations � � � � i ∆ t i ∆ t ϕ j ( r , t + ∆ t ) = exp 2 H ( t + ∆ t ) 2 H ( t ) ϕ j ( r , t ) exp 1 4 A k ϕ ( r ) ∑ exp ( A ) ϕ ( r ) ∼ k = 0 1

main operation: application of the hamiltonian ϕ ( r , t ) → H ( t ) ϕ ( r , t ) H ( t ) = − 1 1 2 ∇ 2 + V KS ( r , t ) 1 finite-difference laplacian

gpu optimization strategy one orbital blocks of at a time orbitals execution units data: KS orbitals X. Andrade and L. Genovese, Harnessing the power of GPUs in Fundamentals of TDDFT, (Springer 2012)

performance of the hamiltonian operator

comparison with the terachem code relative speed­up total calculation time X. Andrade and A. Aspuru-Guzik, JCTC 9 4360-4373 (2013)

multiple-level parallelization k­points / spin orbitals domain decomposition threads gpu threads vectorization X. Andrade et al, JPCM, 126 , 184106 (2012)

multiple gpus in parallel scaling for C 540 fullerene preliminary gpu results communication bottleneck smaller time to solution

conclusions electron dynamics is promising for gpu based supercomputers code improvements required

thanks Erik Draeger Alfredo Correa LLNL computing LLNL LDRD program This work performed under the auspices of the U.S. Department of Energy by Lawrence Livermore National Laboratory under Contract DE-AC52-07NA27344 (IM release number LLNL-PRES-680478)