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Gyrokinetic modeling is appropriate for describing Tokamak plasma turbulence, and the gyroaverage operator is a cornerstone of this approach. In a gyrokinetic code, the gyroaveraging scheme needs to be accurate enough to avoid spoiling the data but also requires a low computation cost because it is applied often on the main unknown, the 5D guiding-center distribution function, and on the 3D electric potentials. In the present paper, we improve a gyroaverage scheme based on Hermite interpolation used in the Gysela code. This initial implementation represents a too large fraction of the total execution time. The gyroaverage operator has been reformulated and is now expressed as a matrix-vector product and a cache-friendly algorithm has been setup. Different techniques have been investigated to quicken the computations by more than a factor two. Description of the algorithms is given, together with an analysis of the achieved performance.

The Projection on Proper elements (PoPe) is a novel method of code control dedicated to 1) checking the correct implementation of models, 2) determining the convergence of numerical methods and 3) characterizing the residual errors of any given solution at very low cost. The basic idea is to establish a bijection between a simulation and a set of equations that generate it. Recovering equations is direct and relies on a statistical measure of the weight of the various operators. This method can be used in any dimensions and any regime, including chaotic ones. This method also provides a procedure to design reduced models and quantify the ratio costs to benefits. PoPe is applied to a kinetic and a fluid code of plasma turbulence.

A novel and generic understanding of spontaneous generation of transport barriers and zonation regimes in turbulent self-organization is presented. It associates the barrier onset to the development of a spectral gap between large scale flows and turbulence modes leading to a zonation regime. A robust barrier builds-up at the interface of such a region and a neighboring one with reduced zonal flow generation. This more complex and generic transition paradigm could fit the numerous and sometimes conflicting observations as in fusion plasma experiments. Barrier relaxation by bursts of turbulence regenerate the zonal flows that are eroded by viscous (collisional-like) damping. The duration of the quiescent phase between the quasi-periodic relaxation events is governed by this damping process, hence the barrier collision frequency for fusion plasmas.

This work describes the challenges presented by porting parts ofthe Gysela code to the Intel Xeon Phi coprocessor, as well as techniques used for optimization, vectorization and tuning that can be applied to other applications. We evaluate the performance of somegeneric micro-benchmark on Phi versus Intel Sandy Bridge. Several interpolation kernels useful for the Gysela application are analyzed and the performance are shown. Some memory-bound and compute-bound kernels are accelerated by a factor 2 on the Phi device compared to Sandy architecture. Nevertheless, it is hard, if not impossible, to reach a large fraction of the peek performance on the Phi device,especially for real-life applications as Gysela. A collateral benefit of this optimization and tuning work is that the execution time of Gysela (using 4D advections) has decreased on a standard architecture such as Intel Sandy Bridge., Comment: submitted to ESAIM proceedings for CEMRACS 2014 summer school version reviewed