Optimization of the Gyroaverage operator based on Hermite interpolation

Abstract

Abstract. 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.

A 5D gyrokinetic full-f global semi-Lagrangian code for flux-driven ion turbulence simulations

“…As shown in [113] the method converges with the number of points, so there is no interest in decreasing the number of points at small radius. It is shown in [104] that 16 points is a good compromise between accuracy and CPU time consumption (2 times slower than the previous Padé approximation due to its higher algorithmic complexity). All numerical results presented in the following are performed with the Padé approximation.…”

A New Parallelization Scheme for the Hermite Interpolation Based Gyroaverage Operator

“…Then a second interpolation along θ is performed from these two new points to reach the target point (r,θ). The coefficients used for the Hermite interpolation are detailed in [6].…”

“…This section presents how the numerical scheme explained in the previous paragraph is implemented in GYSELA according to the work conducted in [6]. We denote N r and N θ , the number of mesh points in the r and θ dimensions.…”

“…Moreover it does not damp the small variations of the function as the Padé approximation did. This new method has previously been implemented in GYSELA [6], replacing the Padé approximation based operator and leading to a great increase in precision and possibilities for better parallelization schemes. However, the transpositions were kept, as it was easier for a first integration in GYSELA to keep the same parallel strategy.…”

Benefits of SMT and of Parallel Transpose Algorithm for the Large-Scale GYSELA Application

“…It can be proved that it is equivalent to apply a Bessel function of first order J0. This gyroaverage operator will not be addressed in this paper but numerical details can be found in [21] and parallelization optimizations for gysela in [19]. The derivatives of J0 φ along the torus dimensions are computed.…”