标题： 三维直角和圆柱坐标系中孤立系统的二阶精度快速泊松求解器 显示英文标题

标题： A Fast Poisson Solver of Second-Order Accuracy for Isolated Systems in Three-Dimensional Cartesian and Cylindrical Coordinates

摘要： 我们提出了一种精确且高效的方法，用于在三维笛卡尔坐标和柱坐标下计算孤立系统在真空（开放）边界条件下的引力势。 我们的方法包括两部分：内部求解器和边界求解器。 内部求解器采用特征函数展开方法结合三对角矩阵求解器，以满足零边界条件来求解泊松方程。 边界求解器采用詹姆斯方法，计算由于屏蔽电荷产生的边界势，这些屏蔽电荷用于保持内部求解器的零边界条件。 完整的引力势计算需要运行内部求解器两次和边界求解器一次。 我们开发了一种在柱坐标下计算离散格林函数的方法，这是维持二阶精度的詹姆斯算法的重要组成部分。 我们将该方法实现到{\tt Athena++}磁流体动力学代码中，并进行了各种测试，以验证我们的求解器具有二阶精度并表现出良好的并行性能。 显示英文摘要

摘要： We present an accurate and efficient method to calculate the gravitational potential of an isolated system in three-dimensional Cartesian and cylindrical coordinates subject to vacuum (open) boundary conditions. Our method consists of two parts: an interior solver and a boundary solver. The interior solver adopts an eigenfunction expansion method together with a tridiagonal matrix solver to solve the Poisson equation subject to the zero boundary condition. The boundary solver employs James's method to calculate the boundary potential due to the screening charges required to keep the zero boundary condition for the interior solver. A full computation of gravitational potential requires running the interior solver twice and the boundary solver once. We develop a method to compute the discrete Green's function in cylindrical coordinates, which is an integral part of the James algorithm to maintain second-order accuracy. We implement our method in the {\tt Athena++} magnetohydrodynamics code, and perform various tests to check that our solver is second-order accurate and exhibits good parallel performance.