Gyroaverage operator for a polar mesh

Steiner, Christophe; Mehrenberger, Michel; Crouseilles, Nicolas; Grandgirard, V.; Latu, Guillaume; Rozar, Fabien

doi:10.1140/epjd/e2014-50211-7

Cited by 14 publications

(32 citation statements)

References 20 publications

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“…The gyroaverage operator depending on the spatial coordinates in the polar plane is defined as follows [21]:…”

Section: Gyroaverage Operatormentioning

confidence: 99%

“…The two functions represent an arbitrary field quantity respectively defined on a grid with polar and Cartesian coordinates. It can be shown [21] that the gyroaverage operator defined in equation (7) can be expressed as a function of the Bessel function of first order, and thus in the Fourier space the gyroaverage is reduced to a multiplication with a Bessel function. In this context though, another approach has been used in order to compute the gyroaverage operator, based on the 2D Lagrangian interpolation.…”

Section: Gyroaverage Operatormentioning

confidence: 99%

See 1 more Smart Citation

Targeting Realistic Geometry in Tokamak Code Gysela

Bouzat¹,

Bressan

Grandgirard

et al. 2018

ESAIM: ProcS

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In magnetically confined plasmas used in Tokamak, turbulence is responsible for specific transport that limits the performance of this kind of reactors. Gyrokinetic simulations are able to capture ion and electron turbulence that give rise to heat losses, but require also state-of-the-art HPC techniques to handle computation costs. Such simulations are a major tool to establish good operating regime in Tokamak such as ITER, which is currently being built. Some of the key issues to address more realistic gyrokinetic simulations are: efficient and robust numerical schemes, accurate geometric description, good parallelization algorithms. The framework of this work is the Semi-Lagrangian setting for solving the gyrokinetic Vlasov equation and the Gysela code. In this paper, a new variant for the interpolation method is proposed that can handle the mesh singularity in the poloidal plane at r = 0 (polar system is used for the moment in Gysela). A non-uniform meshing of the poloidal plane is proposed instead of uniform one in order to save memory and computations. The interpolation method, the gyroaverage operator, and the Poisson solver are revised in order to cope with non-uniform meshes. A mapping that establish a bijection from polar coordinates to more realistic plasma shape is used to improve realism. Convergence studies are provided to establish the validity and robustness of our new approach.

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“…The gyroaverage operator depending on the spatial coordinates in the polar plane is defined as follows [21]:…”

Section: Gyroaverage Operatormentioning

confidence: 99%

Section: Gyroaverage Operatormentioning

confidence: 99%

Targeting Realistic Geometry in Tokamak Code Gysela

Bouzat¹,

Bressan

Grandgirard

et al. 2018

ESAIM: ProcS

Self Cite

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show abstract

“…In the uniform case, we are able to check the linear phase behaviour by solving numerically the dispersion relation and compare the simulation output with it (see also [25,26]). Note that the dispersion relation depends on k : this permits to compare simulations in the oblique and uniform case, in order to check the correctness of the simulations in the oblique case, as we will see.…”

Section: Comparison With Classical (Not Aligned) Approachmentioning

confidence: 99%

Field-Aligned Interpolation for Semi-Lagrangian Gyrokinetic Simulations

et al. 2017

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This work is devoted to the study of field-aligned interpolation in semi-Lagrangian codes. In the context of numerical simulations of magnetic fusion devices, this approach is motivated by the observation that gradients of the solution along the magnetic field lines are typically much smaller than along a perpendicular direction. In toroidal geometry, fieldaligned interpolation consists of a 1D interpolation along the field line, combined with 2D interpolations on the poloidal planes (at the intersections with the field line). A theoretical justification of the method is provided in the simplified context of constant advection on a 2D periodic domain: unconditional stability is proven, and error estimates are given which highlight the advantages of field-aligned interpolation. The same methodology is successfully applied to the solution of the gyrokinetic Vlasov equation, for which we present the ion temperature gradient (ITG) instability as a classical test-case: first we solve this in cylindrical geometry (screw-pinch), and next in toroidal geometry (circular Tokamak). In the first case, the algorithm is implemented in Selalib (semi-Lagrangian library), and the numerical simulations provide linear growth rates that are in accordance with the linear dispersion analysis. In the second case, the algorithm is implemented in the Gysela code, and the numerical simulations are benchmarked with those employing the standard (not aligned) scheme. Numerical experiments show that field-aligned interpolation leads to considerable memory savings for the same level of accuracy; substantial savings are also expected in reactor-scale simulations.

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“…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.…”

Section: Gysela Applicationmentioning

confidence: 99%

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

Latu

Bigot

Bouzat

et al. 2016

Proceedings of the Platform for Advanced Scientific Computing Conference

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This article describes how we manage to increase performance and to extend features of a large parallel application through the use of simultaneous multithreading (SMT) and by designing a robust parallel transpose algorithm. The semi-Lagrangian code Gysela typically performs large physics simulations using a few thousands of cores, between 1k cores up to 16k on x86-based clusters. However, simulations with finer resolutions and with kinetic electrons increase those needs by a huge factor, providing a good example of applications requiring Exascale machines. To improve Gysela compute times, we take advantage of efficient SMT implementations available on recent INTEL architectures. We also analyze the cost of a transposition communication scheme that involves a large number of cores in our case. Adaptation of the code for balance load whenever using both SMT and good deployment strategy led to a significant reduction that can be up to 38% of the execution times.

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Gyroaverage operator for a polar mesh

Cited by 14 publications

References 20 publications

Targeting Realistic Geometry in Tokamak Code Gysela

Targeting Realistic Geometry in Tokamak Code Gysela

Field-Aligned Interpolation for Semi-Lagrangian Gyrokinetic Simulations

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

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