标题： 一种用于多维时间依赖输运方程的自适应多分辨率不连续伽辽金方法 显示英文标题

标题： An Adaptive Multiresoluton Discontinuous Galerkin Method for Time-Dependent Transport Equations in Multi-dimensions

摘要： 在本文中，我们开发了一种自适应多分辨率不连续伽辽金（DG）方案，用于多维时间依赖的输运方程。该方法使用张量化嵌套网格上的多小波构建。自适应性通过基于层次剩余的误差阈值实现，Runge-Kutta DG（RKDG）方案被用作参考时间演化算法。我们证明了当解是光滑的时候，该方案的表现类似于稀疏网格DG方法，在多维情况下减少了计算成本。当解不再光滑时，自适应算法可以自动捕捉细小的局部结构。因此，该方法非常适合确定性动力学模拟。提供了包括多个基准测试、Vlasov-Poisson（VP）和振荡VP系统的数值结果。 显示英文摘要

摘要： In this paper, we develop an adaptive multiresolution discontinuous Galerkin (DG) scheme for time-dependent transport equations in multi-dimensions. The method is constructed using multiwavlelets on tensorized nested grids. Adaptivity is realized by error thresholding based on the hierarchical surplus, and the Runge-Kutta DG (RKDG) scheme is employed as the reference time evolution algorithm. We show that the scheme performs similarly to a sparse grid DG method when the solution is smooth, reducing computational cost in multi-dimensions. When the solution is no longer smooth, the adaptive algorithm can automatically capture fine local structures. The method is therefore very suitable for deterministic kinetic simulations. Numerical results including several benchmark tests, the Vlasov-Poisson (VP) and oscillatory VP systems are provided.