Analysis and compression of six-dimensional gyrokinetic datasets using higher order singular value decomposition

Hatch, D. R.; Del-Castillo-Negrete, Diego B; Terry, P. W.

doi:10.1016/j.jcp.2012.02.007

Cited by 17 publications

(7 citation statements)

References 35 publications

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“…for parallel velocity space, where H m (x) is the mth order Hermite polynomial. Hermite polynomials were shown empirically to be an efficient representation of velocity space in gyrokinetic simulations in [43]. Their use in this work was inspired, in particular, by earlier demonstrations of their utility in calculating linear eigenmode spectra [44,50].…”

Section: Modelmentioning

confidence: 99%

Linear signatures in nonlinear gyrokinetics: interpreting turbulence with pseudospectra

et al. 2016

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A notable feature of plasma turbulence is its propensity to retain features of the underlying linear eigenmodes in a strongly turbulent state-a property that can be exploited to predict various aspects of the turbulence using only linear information. In this context, this work examines gradient-driven gyrokinetic plasma turbulence through three lenses-linear eigenvalue spectra, pseudospectra, and singular value decomposition (SVD). We study a reduced gyrokinetic model whose linear eigenvalue spectra include ion temperature gradient driven modes, stable drift waves, and kinetic modes representing Landau damping. The goal is to characterize in which ways, if any, these familiar ingredients are manifest in the nonlinear turbulent state. This pursuit is aided by the use of pseudospectra, which provide a more nuanced view of the linear operator by characterizing its response to perturbations. We introduce a new technique whereby the nonlinearly evolved phase space structures extracted with SVD are linked to the linear operator using concepts motivated by pseudospectra. Using this technique, we identify nonlinear structures that have connections to not only the most unstable eigenmode but also subdominant modes that are nonlinearly excited. The general picture that emerges is a system in which signatures of the linear physics persist in the turbulence, albeit in ways that cannot be fully explained by the linear eigenvalue approach; a nonmodal treatment is necessary to understand key features of the turbulence.

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Section: Modelmentioning

confidence: 99%

Linear signatures in nonlinear gyrokinetics: interpreting turbulence with pseudospectra

et al. 2016

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“…Hermite polynomials provide an elegant characterization of energy transfer and dissipation in parallel velocity scales [17,18]. Moreover, they have recently been shown to optimally represent velocity space in gyrokinetic simulations [19] and to facilitate accurate solutions of linear kinetic operators [20]. The resulting gyrokinetic equation reads [21] PRL 111, 175001 (2013) P H Y S I C A L R E V I E W L E T T E R S week ending 25 OCTOBER 2013 @f k;n @t…”

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confidence: 99%

Transition between Saturation Regimes of Gyrokinetic Turbulence

et al. 2013

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A gyrokinetic model of ion temperature gradient driven turbulence in magnetized plasmas is used to study the injection, nonlinear redistribution, and collisional dissipation of free energy in the saturated turbulent state over a broad range of driving gradients and collision frequencies. The dimensionless parameter L(T)/L(C), where L(T) is the ion temperature gradient scale length and L(C) is the collisional mean free path, is shown to parametrize a transition between a saturation regime dominated by nonlinear transfer of free energy to small perpendicular (to the magnetic field) scales and a regime dominated by dissipation at large scales in all phase space dimensions.

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“…Methods for reducing the computational cost of tensor trains are discussed in [58,59,55]. Applications to the Vlasov kinetic equation can be found in [60,61,62].…”

Section: Hierarchical Tuckermentioning

confidence: 99%

Parallel tensor methods for high-dimensional linear PDEs

Boelens

Venturi

Tartakovsky

2018

Journal of Computational Physics

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High-dimensional partial-differential equations (PDEs) arise in a number of fields of science and engineering, where they are used to describe the evolution of joint probability functions. Their examples include the Boltzmann and Fokker-Planck equations. We develop new parallel algorithms to solve high-dimensional PDEs. The algorithms are based on canonical and hierarchical numerical tensor methods combined with alternating least squares and hierarchical singular value decomposition. Both implicit and explicit integration schemes are presented and discussed. We demonstrate the accuracy and efficiency of the proposed new algorithms in computing the numerical solution to both an advection equation in six variables plus time and a linearized version of the Boltzmann equation.

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Analysis and compression of six-dimensional gyrokinetic datasets using higher order singular value decomposition

Cited by 17 publications

References 35 publications

Linear signatures in nonlinear gyrokinetics: interpreting turbulence with pseudospectra

Linear signatures in nonlinear gyrokinetics: interpreting turbulence with pseudospectra

Transition between Saturation Regimes of Gyrokinetic Turbulence

Parallel tensor methods for high-dimensional linear PDEs

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