论文标题
（等离子体）动力学方程的无别名，无基质和不连续的不连续的Galerkin算法
Alias-free, matrix-free, and quadrature-free discontinuous Galerkin algorithms for (plasma) kinetic equations
论文作者
论文摘要
了解基本动力学过程对于从血浆物理学到气体动态的许多问题很重要。针对这些问题的第一原理方法需要通过Boltzmann方程进行统计描述，并结合适当的场方程。在本文中，我们介绍了不连续的Galerkin（DG）算法的新颖版本，以求解此类动力学方程。与蒙特卡洛方法不同，我们使用连续方案，在该方案中，我们使用不连续的基础函数直接离散6D相位空间。我们的DG方案消除了计数噪声和混叠误差，否则会污染精致的田间粒子相互作用。我们使用具有降低自由度的模态基础函数，以提高效率，同时保留高正式的收敛顺序。我们的实施结合了许多软件创新：使用JIT编译的顶级语言，自动生成的计算内核和复杂的共享模式MPI实现来处理速度空间并行化。
Understanding fundamental kinetic processes is important for many problems, from plasma physics to gas dynamics. A first-principles approach to these problems requires a statistical description via the Boltzmann equation, coupled to appropriate field equations. In this paper we present a novel version of the discontinuous Galerkin (DG) algorithm to solve such kinetic equations. Unlike Monte-Carlo methods we use a continuum scheme in which we directly discretize the 6D phase-space using discontinuous basis functions. Our DG scheme eliminates counting noise and aliasing errors that would otherwise contaminate the delicate field-particle interactions. We use modal basis functions with reduced degrees of freedom to improve efficiency while retaining a high formal order of convergence. Our implementation incorporates a number of software innovations: use of JIT compiled top-level language, automatically generated computational kernels and a sophisticated shared-memory MPI implementation to handle velocity space parallelization.
