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The NVIDIA Volta GPU microarchitecture introduces a specialized unit, called Tensor Core that performs one matrix-multiplyand-accumulate on 4×4 matrices per clock cycle. The NVIDIA Tesla V100 accelerator, featuring the Volta microarchitecture, provides 640 Tensor Cores with a theoretical peak performance of 125 Tflops/s in mixed precision. In this paper, we investigate current approaches to program NVIDIA Tensor Cores, their performances and the precision loss due to computation in mixed precision.Currently, NVIDIA provides three different ways of programming matrix-multiply-and-accumulate on Tensor Cores: the CUDA Warp Matrix Multiply Accumulate (WMMA) API, CUTLASS, a templated library based on WMMA, and cuBLAS GEMM. After experimenting with different approaches, we found that NVIDIA Tensor Cores can deliver up to 83 Tflops/s in mixed precision on a Tesla V100 GPU, seven and three times the performance in single and half precision respectively. A WMMA implementation of batched GEMM reaches a performance of 4 Tflops/s. While precision loss due to matrix multiplication with half precision input might be critical in many HPC applications, it can be considerably reduced at the cost of increased computation. Our results indicate that HPC applications using matrix multiplications can strongly benefit from using of NVIDIA Tensor Cores.

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The primary target of the Magnetospheric MultiScale (MMS) mission is the electron-scale di usion layer around reconnection sites. Here we study where these regions are found in full three-dimensional simulations. In two dimensions the sites of electron di usion, defined as the regions where magnetic topology changes and electrons move with respect to the magnetic field lines, are located near the reconnection site. But in three dimensions we find that the reconnection exhaust far from the primary reconnection site also becomes host to secondary reconnection sites. Four diagnostics are used to demonstrate the point: the direct observation of topology impossible without secondary reconnection, the direct measurement of topological field line breakage, the measurement of electron jets emerging from secondary reconnection regions, and the violation of the frozen-in condition. We conclude that secondary reconnection occurs in a large part of the exhaust, providing many more chances for MMS to find itself in the right region to hit its target.T he primary focus of the planned Magnetospheric MultiScale (MMS) Mission 1 is the identification and in situ study of electron-scale regions where magnetic reconnection develops (http://mms.gsfc.nasa.gov/science.html). Magnetic reconnection 2 is believed to be the engine of many space and astrophysical processes where magnetic energy is stored over relatively long times to be released suddenly in bursts of kinetic energy. The mission planning and the thinking of the community has been in large part informed by the two-dimensional (2D) picture that has emerged from decades of simulations based on the classic field reversal configuration, where two regions of oppositely directed magnetic fields reconnect at one central location called the x-point. There magnetic field lines break and form new connections.This paradigm has been tremendously successful and from 2D simulations has found confirmation in many laboratory experiments 3 and in situ space observations 4 . When going from two to three dimensions, the model still remains valid if one can assume the presence of a region where the variations along the out-of-plane directions are small. In this case, extended reconnection regions develop, retaining a 2D-like configuration over significant widths in the out-of-plane direction 5,6 . But 3D effects can drastically alter the structure of a reconnection site 7 , with the possibility of inherently 3D configurations even in fast kinetic reconnection 8 .We think it is imperative to ask the question as to how these new 3D discoveries impact the execution of the MMS mission. The mission was designed with the two-nested-box vision 9 : around the reconnection site the ions become decoupled from magnetic field lines in a larger region, whereas the electrons continue to move along with the field lines until a smaller inner region is reached. This scheme is etched into the minds of every researcher working in reconnection and appears in the place of honour in the science section of the MMS web...

A new Particle-in-Cell (PIC) method, that conserves energy exactly, is presented. The particle equations of motion and the Maxwell's equations are differenced implicitly in time by the midpoint rule and solved concurrently by a Jacobian-free Newton Krylov (JFNK) solver. Several tests show that the finite grid instability is eliminated in energy conserving PIC simulations, and the method correctly describes the two-stream and Weibel instabilities, conserving exactly the total energy. The computational time of the energy conserving PIC method increases linearly with the number of particles, and it is rather insensitive to the number of grid points and time step. The kinetic enslavement technique can be effectively used to reduce the problem matrix size and the number of JFNK solver iterations.

We have recently developed a new modeling capability to embed the implicit particle‐in‐cell (PIC) model iPIC3D into the Block‐Adaptive‐Tree‐Solarwind‐Roe‐Upwind‐Scheme magnetohydrodynamic (MHD) model. The MHD with embedded PIC domains (MHD‐EPIC) algorithm is a two‐way coupled kinetic‐fluid model. As one of the very first applications of the MHD‐EPIC algorithm, we simulate the interaction between Jupiter's magnetospheric plasma and Ganymede's magnetosphere. We compare the MHD‐EPIC simulations with pure Hall MHD simulations and compare both model results with Galileo observations to assess the importance of kinetic effects in controlling the configuration and dynamics of Ganymede's magnetosphere. We find that the Hall MHD and MHD‐EPIC solutions are qualitatively similar, but there are significant quantitative differences. In particular, the density and pressure inside the magnetosphere show different distributions. For our baseline grid resolution the PIC solution is more dynamic than the Hall MHD simulation and it compares significantly better with the Galileo magnetic measurements than the Hall MHD solution. The power spectra of the observed and simulated magnetic field fluctuations agree extremely well for the MHD‐EPIC model. The MHD‐EPIC simulation also produced a few flux transfer events (FTEs) that have magnetic signatures very similar to an observed event. The simulation shows that the FTEs often exhibit complex 3‐D structures with their orientations changing substantially between the equatorial plane and the Galileo trajectory, which explains the magnetic signatures observed during the magnetopause crossings. The computational cost of the MHD‐EPIC simulation was only about 4 times more than that of the Hall MHD simulation.

Collisionless shock nonstationarity arising from microscale physics influences shock structure and particle acceleration mechanisms. Nonstationarity has been difficult to quantify due to the small spatial and temporal scales. We use the closely spaced (subgyroscale), high-time-resolution measurements from one rapid crossing of Earth's quasiperpendicular bow shock by the Magnetospheric Multiscale (MMS) spacecraft to compare competing nonstationarity processes. Using MMS's high-cadence kinetic plasma measurements, we show that the shock exhibits nonstationarity in the form of ripples.

We analyze the signatures of component reconnection for a Harris current sheet with a guide field using the physical mass ratio of hydrogen. The study uses the fully kinetic particle in cell code IPIC3D to investigate the scaling with mass ratio of the following three main component reconnection features: electron density cavities along the separatrices, channels of fast electron flow within the cavities, and electron phase space holes due to the Buneman instability in the electron high speed channels. The width and strength of the electron holes and of the electron cavities are studied up the mass ratio proper of hydrogen, considering the effect of the simulation box size, and of the boundary conditions. The results compare favorably with the existing data from the Cluster and Themis missions and provide quantitative predictions for realistic conditions to be encountered by the planned magnetospheric multiscale mission.