三维空间电荷模拟中纵向周期性和横向开边界条件下的快速Poisson解
A Fast 3D Poisson Solver with Longitudinal Periodic and Transverse Open Boundary Conditions for Space-Charge Simulations
摘要：
具有纵向周期性和横向开边界条件的三维泊松方程在粒子加速器束流物理中具有重要的应用。本文提出了一种用谱有限差分法求解泊松方程的快速有效方法。该方法使用仅包含带电粒子束的计算域，并且具有$O(N_u(logN_{mode}))$的计算复杂度，其中$N_u$是未知数的总数，并且$N_{mode}$是纵向或方位角模式的最大数量。这节省了计算时间和内存的使用，通过使用人工边界条件在一个大的扩展计算域。
英文摘要：
A three-dimensional (3D) Poisson solver with longitudinal periodic and transverse open boundary conditions can have important applications in beam physics of particle accelerators. In this paper, we present a fast efficient method to solve the Poisson equation using a spectral finite-difference method. This method uses a computational domain that contains the charged particle beam only and has a computational complexity of $O(N_u(logN_{mode}))$, where $N_u$ is the total number of unknowns and $N_{mode}$ is the maximum number of longitudinal or azimuthal modes. This saves both the computational time and the memory usage by using an artificial boundary condition in a large extended computational domain.
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