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We study the stability and instability of Langmuir waves propagating in a hot, unmagnetized plasma modeled by the Vlasov–Poisson system and encompassing a variety of velocity distributions, including perturbations of Lorentzian, Kappa, and incomplete Maxwellian steady states. The influence of both high-frequency spatial perturbations and physical parameters on the rate of growth or decay of the plasma response to the initial perturbation is elucidated. Our methods do not rely upon analytic approximation, but instead feature a numerical approximation of the roots of the associated dielectric function that can be accurately quantified without the need for prior assumptions on the parameter regimes under consideration. In this way, the computational discovery of so-called “active” subspaces in the parameter space allows one to identify and quantify the uncertainty generated by physical parameters on the stability properties of wave-like perturbations in a collisionless plasma. 

Abstract. Lagrangian particle tracking schemes allow a wide range of flow and transport processes to be simulated accurately, but a major challenge is numerically implementing the inter-particle interactions in an efficient manner. This article develops a multi-dimensional, parallelized domain decomposition (DDC) strategy for mass-transfer particle tracking (MTPT) methods in which particles exchange mass dynamically. We show that this can be efficiently parallelized by employing large numbers of CPU cores to accelerate run times. In order to validate the approach and our theoretical predictions we focus our efforts on a well-known benchmark problem with pure diffusion, where analytical solutions in any number of dimensions are well established. In this work, we investigate different procedures for “tiling” the domain in two and three dimensions (2-D and 3-D), as this type of formal DDC construction is currently limited to 1-D. An optimal tiling is prescribed based on physical problem parameters and the number of available CPU cores, as each tiling provides distinct results in both accuracy and run time. We further extend the most efficient technique to 3-D for comparison, leading to an analytical discussion of the effect of dimensionality on strategies for implementing DDC schemes. Increasing computational resources (cores) within the DDC method produces a trade-off between inter-node communication and on-node work.For an optimally subdivided diffusion problem, the 2-D parallelized algorithm achieves nearly perfect linear speedup in comparison with the serial run-up to around 2700 cores, reducing a 5 h simulation to 8 s, while the 3-D algorithm maintains appreciable speedup up to 1700 cores.