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November 16, 2013

SC13 Research Highlight: Extreme Scale Plasma Turbulence Simulation

Bei Wang, Stephane Ethier & William Tang
Electrostatic field in magnetically confined plasmas (Image courtesy of Kwan-Liu Ma, UC Davis)

As the global energy economy makes the transition from fossil fuels toward cleaner alternatives, fusion becomes an attractive potential solution for satisfying the growing needs. Fusion energy, which is the power source for the sun, can be generated on earth, for example, in magnetically-confined laboratory plasma experiments (called “tokamaks”) when the isotopes of hydrogen (e.g., deuterium and tritium) combine to produce an energetic helium “alpha” particle and a fast neutron – with an overall energy multiplication factor of 450:1.

Building the scientific foundations needed to develop fusion power demands high-physics-fidelity predictive simulation capability for magnetically-confined fusion energy (MFE) plasmas. To do so in a timely way requires utilizing the power of modern supercomputers to simulate the complex dynamics governing MFE systems — including ITER, a multi-billion dollar international burning plasma experiment supported by 7 governments representing over half of the world’s population.

Unavoidable spatial variations in such systems produce microturbulence which can significantly increase the transport rate of heat, particles, and momentum across the confining magnetic field in tokamak devices.  Since the balance between these energy losses and the self-heating rates of the actual fusion reactions will ultimately determine the size and cost of an actual fusion reactor, understanding and possibly controlling the underlying physical processes is key to achieving the efficiency needed to help ensure the practicality of future fusion reactors.

The goal here is to gain new physics insights on MFE confinement scaling by making effective use of powerful world-class supercomputing systems such as the IBM Blue-Gene-Q “Mira” at the Argonne Leadership Class Facility (ALCF). Associated knowledge gained addresses the key question of how turbulent transport and associated confinement characteristics scale from present generation devices to the much larger ITER-scale plasmas. This involves the development of modern software capable of using leadership class supercomputers to carry out reliable first principles-based simulations of multi-scale tokamak plasmas.  The fusion physics challenge here is that the key decade-long MFE estimates of confinement scaling with device size (the so-called “Bohm to Gyro-Bohm” “rollover” trend caused by the ion temperature gradient instability) demands much higher resolution to be realistic/reliable.  Our important new fusion physics finding is that this “rollover” is much more gradual than established earlier in far lower resolution, shorter duration studies with magnitude of transport now reduced by a factor of two.

The basic particle method has long been a well established approach that simulates the behavior of charged particles interacting with each other through pair-wise electromagnetic forces.  At each time step, the particle properties are updated according to these calculated forces.  For applications on powerful modern supercomputers with deep cache hierarchy, a pure particle method is very efficient with respect to locality and arithmetic intensity (compute bound). Unfortunately, the O(N2 ) complexity makes a particle method impractical for plasma simulations using millions of particles per process.  Rather than calculating O(N2) forces, the particle-in-cell (PIC) method, which was introduced by J. Dawson and N. Birdsall in 1968, employs a grid as the media to calculate the long range electromagnetic forces.  This reduces the complexity from O(N2) to O(N+MlogM), where M is the number of grid points and is usually much smaller than N.  Specifically, the PIC simulations are being carried out using “macro” particles (~103 times the radius of a real charged ion particle) with characteristic properties, including position, velocity and weight.  However, achieving high parallel and architectural efficiency is very challenging for a PIC method due to potential fine-grained data hazards, irregular data access, and low arithmetic intensity.  The issue gets more severe as the HPC community moves into the future to address even more radical changes in computer architectures as the multicore and manycore revolution progresses.

Machines such as the IBM BG/Q Mira demand at least 49,152-way MPI parallelism and up to 3 million-way thread-level parallelism in order to fully utilize the system. While distributing particles to at least 49,152 processes is straightforward, the distribution of a 3D torus-shape grid among those processes is non-trivial. For example, first consider the 3D torus as being decomposed into sub-domains of uniform volume.  In a circular geometry, the sub-domains close to the edge of the system will contain more grid points than the core. This leads to potential load imbalance issues for the associated grid-based work.

Through a close collaboration with the Future Technologies Group at the Lawrence Berkeley National Laboratory, we have developed and optimized a new version of the Gyrokinetic Toroidal Code (“GTC-Princeton” or “GTC-P”) to address the challenges in the PIC method for leadership-class systems in the multicore/manycore regime.  GTC-P includes multiple levels of parallelism, a 2D domain decomposition, a particle decomposition, and a loop level parallelism implemented with OpenMP – all of which help enable this state-of-the-art PIC code to efficiently scale to the full capability of the largest extreme scale HPC systems currently available. Special attention has been paid to the load imbalance issue associated with domain decomposition. To improve single node performance, we select a “structure-of-arrays” (SOA) data layout for particle data, align memory allocation to facilitate SIMD intrinsic, binning particles to improve locality, and use loop fusion to improve arithmetic intensity. We also manually flatten irregular nested loop to expose more parallelization to OpenMP threads. GTC-P features a two-dimensional topology for point-to-point communication. On the IBM BG/Q system with 5D torus network, we have optimized communication with customized process mapping. Data parallelism is also being continuously exploited through SIMD intrinsics (e.g., QPX intrinsics on IBM BG/Q) and by improving data movement through software pre-fetching.

Simulations of confinement physics for large-scale MFE plasmas have been carried out for the first time with very high phase-space resolution and long temporal duration to deliver important new scientific insights. This was enabled by the new “GTC-P” code which was developed to use multi-petascale capabilities on world-class systems such as the IBM BG-Q  “Mira” @ ALCF  and also “Sequoia” @ LLNL.  (Accomplishments are summarized in the two figures below.)

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Figure 1:  Modern GTC-Princeton (GTC-P) Code Performance on World-Class IBM BG-Q Systems

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Figure 2:  Important new scientific discoveries enabled by harnessing modern supercomputing capabilities at extreme scale

The success of these projects were greatly facilitated by the fact that true interdisciplinary collaborative effort with Computer Science and Applied Math scientists have produced modern C and CUDA versions of the key HPC code (originally written — as in the case of the vast majority of codes in the FES application domain) in Fortran-90.  The demonstrated capability to run at scale on the largest open-science IBM BG-Q system (“Mira” at the ALCF) opened the door to obtain access to NNSA’s “Sequoia” system at LLNL – which then produced the outstanding results shown on Figure 1.  More recently, excellent performance of the GPU-version of GTC-P has been demonstrated on the “Titan” system at the Oak Ridge Leadership Class Facility (OLCF).  Finally, the G8-sponsored international R&D advances have enabled this project to gain collaborative access to a number of the top international supercomputing facilities — including the Fujitsu K Computer, Japan’s #1 supercomputer.   In addition, these highly visible accomplishments have very recently enabled this project to begin collaborative applications on China’s new Tianhe-2 (TH-2) Intel-MIC-based system – the #1 supercomputing system worldwide.

RESEARCH TEAM:  Bei Wang (Princeton U), Stephane Ethier (PPPL), William Tang (Princeton U/PPPL), K. Ibrahim, S. Williams, L. Oliker (LBNL), K. Madduri (Penn State U), Tim Williams (ANL)

Link to SC13 conference: http://sc13.supercomputing.org/schedule/event_detail.php?evid=pap402

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