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4 applications sustain 1 petaflop on Blue Waters

Four large-scale science applications (VPIC, PPM, QMCPACK and SPECFEM3DGLOBE) have sustained performance of 1 petaflop or more on the Blue Waters supercomputer, and the Weather Research & Forecasting (WRF) run on Blue Waters is the largest WRF simulation ever documented. These applications are part of the NCSA Blue Waters Sustained Petascale Performance (SPP) suite and represent valid scientific workloads.


VPIC integrates the relativistic Maxwell-Boltzmann system in a linear background medium for multiple particle species, in time with an explicit-implicit mixture of velocity Verlet, leapfrog, Boris rotation and exponential differencing based on a reversible phase-space volume conserving second order Trotter factorization. The Petascale Computing Resource Allocation (PRAC) team led by Homayoun Karimabadi (University of California-San Diego) is using VPIC in for kinetic simulations of magnetic reconnection of high temperature plasmas (H+ and e). Magnetic reconnection is an energy conversion process that occurs within high-temperature plasmas and often produces an explosive release of energy as magnetic fields are reconfigured and destroyed. Simulated here are force-free current sheets, thought to be relevant to the solar atmosphere and many astrophysical problems. NCSA and Cray worked to improve compiler optimization of loops not already using optimized vector compiler intrinsic functions, optimizations to eliminate extra data copies, added FMA4 compiler intrinsic functions to improve compute performance and used Cray I/O buffering functionality. The three-dimensional, nearest-neighbor communication maps well to the Gemini network. The VPIC science problem had a 3,072 x 3,072 x 2,464 cell domain with 7.44103E+12 (7 trillion) particles. The science problem was run on 22,528 nodes with 180,224 MPI ranks with 4 OMP threads/rank, and achieved 1.25 PFLOPS sustained over 2.5 hrs.


The PRAC team led by Paul Woodward (University of Minnesota-Twin Cities) is using its hydrodynamics code based on the Piecewise-Parabolic Method (PPM) and Piecewise-Parabolic Boltzmann (PPB) scheme for multifluid volume fraction advection to simulate inertial confinement fusion (ICF) at unprecedented grid resolution. The ICF problem, like the giant star problem the team solved on the Blue Waters Early Science System (ESS), involves turbulent mixing due to instabilities at multi-fluid interfaces, and in both problems the details of this mixing affect the combustion that results. The ICF problem exercises all the features of the PPM codes, including strong shocks and very elaborate treatments of unstable multi-fluid interfaces, while at the same time performing an important scientific problem that has a highly transient character. PPM is designed to be a high-performing application. The Woodward PRAC team has taken significant steps to take advantage of many processor architecture features, including aggressive pipelining, compiler generated SIMD vectorization, minimizing working set size, and shared L3 cache optimization. Communication is primarily halo exchanges on a 3D Cartesian mesh which are overlapped by computations, as is the I/O. The Cray Fortran compiler generated highly vectorized code and provided high-performance math functions. Cray implemented a rank reordering scheme to interleave the I/O server tasks in the MPI rank list. Lustre striping was set as appropriate for the larger output files.

The test case uses a 10,5603 zone mesh—more than 1 trillion cells. It was run across 702,784 cores of Blue Waters, with 681,472 worker threads organized into eight threads per MPI task. In total, 87,846 MPI ranks were running on 21,962 nodes, organized into 1,331 “teams,” each with its own object storage target (OST) for I/O control. The total simulation completed in just under 41 hours of wall time and sustained 1.5 PF/s. More than 587 TB of data was saved with an aggregate of over 17 GB/sec I/O rate. Communication and I/O are essentially 100% overlapped with computation.


The PRAC team led by Shiwei Zhang (College of William and Mary) is using the QMCPACK application on Blue Waters. QMCPACK uses quantum Monte Carlo methods to solve the many-body Schrödinger equation by stochastically sampling the configuration domain. First, a Variational Monte Carlo (VMC) algorithm is used to quickly find a “ballpark” estimate of the solution, and then a Diffusion Monte Carlo (DMC) algorithm is used to refine the estimate from the VMC phase. A number of VMC walkers (each a complete state representation) that randomly move through the energy domain each time step are sampled to create walkers for the DMC phase. The output of the DMC phase is the lowest energy state within a statistical uncertainty, which can be reduced by taking more samples (i.e., using more DMC walkers). Recent predictions using density functional theory (DFT) suggest that hydrogen may be in a superconducting state that could extend from a zero temperature solid state phase to a room temperature metallic liquid. For the test problem the input is for a hydrogen structure under high pressure with VMC only. Cray, NCSA and the QMCPACK team worked on several improvements to an already well-performing code. To fully benefit from the AMD Interlagos processor, FMA4 compiler intrinsics were added to key routines and the AMD version of the math library (libm) was used to replace the GNU release. QMCPACK was run with a 432-atom high-pressure hydrogen problem on 22,500 XE nodes with 4 MPI ranks per node and 8 OpenMP threads per rank. The run achieved sustained performance of 1.037 PF/s for less than 1 hour of execution.


The SPECFEM3D series of codes is a simulation of seismic wave propagation in the earth, modeling the globe as a finite element mesh. While some of the codes model a region of the earth in isolation, SPECFEM3D_GLOBE models propagation of waves from earthquakes through the entire earth and is designed to scale to systems with hundreds of thousands of processor threads. The code takes seismographs and inverts them to synthesize what the displacement was at the epicenter of the earthquake. This is used, among other things, to model the displacement of a close-by earthquake to understand how buildings need to be constructed to withstand earthquakes. The goal for the model problem is to run at a high enough resolution that the shortest period of accurately simulated seismic waves is below the “two second barrier,” or ideally down to a shortest period of 1 second. The runtime process involves two phases: the mesh generation and the solver. The mesh for a SPECFEM3D_GLOBE simulation is based upon a mapping from the cube to the sphere called the cubed sphere that breaks the globe into six chunks, each of which is further subdivided. The spectral-element method solver is a continuous Galerkin technique with optimized efficiency because of its tensorized basis functions and has very good accuracy and convergence properties. NCSA improved the mesher performance by using system memory to store the mesh files for each MPI rank and MPI task reordering reduced communication overhead for both the mesh generator and the solver. Optimizations applied to the solver consisted of a small number of compiler directives to improve the generally excellent vectorization done by the Fortran compiler. These compiler directives inhibited overall aggressive loop unrolling and reordering in a few places. Higher-level optimizations by subroutine inlining were also helpful. The run was done on 21,675 XE nodes with 693,600 MPI ranks and sustained over 1 PF/s.


The Weather Research & Forecasting (WRF) Model is a next-generation mesoscale numerical weather prediction system designed to serve both operational forecasting and atmospheric research needs. It features multiple dynamical cores, a three-dimensional variational (3DVAR) data assimilation system, and a software architecture allowing for computational parallelism and system extensibility. WRF is suitable for a broad spectrum of applications across scales ranging from meters to thousands of kilometers and is the major mesoscale weather forecasting model used by thousands of registered users across the globe.

A model of Hurricane Sandy has been run on 11,400 nodes of Blue Waters (~250 TFLOPS sustained) using a horizontal grid of 9,120 x 9,216 with 48 levels in the vertical domain, for a total of about 4 billion points. The optimal MPI task layout is 16 per node, with 2 OpenMP threads per module. The SPP benchmark for acceptance was run on 4,560 nodes as a 190 x 384 MPI task layout (2 OpenMP threads each), sustaining over 24 GF per node.

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