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.

翻译：血浆流流的精确数字模拟是聚合研究的资产和挑战之一。 对于基于网格的溶液来说,由于维度的诅咒,往往无法取得足够精细的分辨率。稀疏的网格组合技术为减轻运动模拟的维度诅咒提供了手段。然而,与最先进的帽子功能相结合的分级表示方式有不良的保存特性和数字不稳定。目前的工作引入了两种供结合技术使用的分级多级基函数的新变体:双向和完全加权基。新基功能保存总质量,并显示显著提高常态倾斜定量溶液的精度。基于半Lagrangian Vlasov-Poisson溶解剂的合并技术的进一步数字实验显示了在模拟中新基的稳定性效应。