EXAHD: A Massively Parallel Fault Tolerant Sparse Grid Approach for High-Dimensional Turbulent Plasma Simulations

Lago, Rafael; Obersteiner, Michael; Pollinger, Theresa; Rentrop, Johannes; Bungartz, Hans‐Joachim; Dannert, T.; Griebel, Michael; Jenko, F.; Pflüger, Dirk

doi:10.1007/978-3-030-47956-5_11

Cited by 3 publications

(3 citation statements)

References 14 publications

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“…It combines differently resolved numerical solutions multiple times throughout the course of the simulation. The combination technique allows to re-use existing solvers in a blackbox fashion and adds an extra level of parallelism to the parallelism that may already be present in the solver [27]. For instance, previous work applying the gyrokinetic solver GENE [21] has shown that the eigenvalues in the linear part of the simulation can be obtained by a combination technique solution [25].…”

Section: The Curse Of Dimensionality In Kinetic Simulationsmentioning

confidence: 99%

“…This is similar to the inclusion exclusion principle from combinatorics. For example, for the classical sparse grid (27) in 2D this leads to the combination formula…”

Section: The Combination Techniquementioning

confidence: 99%

“…This is why, in our simulations of the Vlasov-Poisson system, we assess the quality of the combined solution by analyzing its performance in two benchmark problems via the time traces of the potential energy. A similar approach was taken in [27] for simulations of the gyrokinetic equations with the code GENE [21].…”

Section: The Combination Techniquementioning

confidence: 99%

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A mass-conserving sparse grid combination technique with biorthogonal hierarchical basis functions for kinetic simulations

Pollinger¹,

Rentrop²,

Pflüger³

et al. 2022

Preprint

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The exact numerical simulation of plasma turbulence is one of the assets and challenges in fusion research. For grid-based solvers, sufficiently fine resolutions are often unattainable due to the curse of dimensionality. The sparse grid combination technique provides the means to alleviate the curse of dimensionality for kinetic simulations. However, the hierarchical representation for the combination step with the state-of-the-art hat functions suffers from poor conservation properties and numerical instability.The present work introduces two new variants of hierarchical multiscale basis functions for use with the combination technique: the biorthogonal and full weighting bases. The new basis functions conserve the total mass and are shown to significantly increase accuracy for a finite-volume solution of constant advection. Further numerical experiments based on the combination technique applied to a semi-Lagrangian Vlasov-Poisson solver show a stabilizing effect of the new bases on the simulations.

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Section: The Curse Of Dimensionality In Kinetic Simulationsmentioning

confidence: 99%

“…This is similar to the inclusion exclusion principle from combinatorics. For example, for the classical sparse grid (27) in 2D this leads to the combination formula…”

Section: The Combination Techniquementioning

confidence: 99%