Kinetic Particle In Cell (PIC) methods can extend greatly their range of applicability if implicit time differencing and spatial adaption are used to address the wide range of time and length scales typical of plasmas. For implicit differencing, we refer the reader to our recent summary of the implicit moment PIC method implemented in our CELESTE3D code [G. Lapenta, Phys. Plasmas, 13, 055904 (2006)]. Instead, the present document deals with the issue of PIC spatial adaptation. Adapting a kinetic PIC code requires two tasks: adapting the grid description of the fields and moments and adapting the particle description of the distribution function. Below we address both issues. First, we describe how grid adaptation can be guided by appropriate measures of the local accuracy of the solution. Based on such information, grid adaptation can be obtained by moving grid points from regions of lesser interest to regions of higher interest or by adding and removing points. We discuss both strategies. Second, we describe how to adapt the local number of particles to reach the required statistical variance in the description of the particle population. Finally two typical applications of adaptive PIC are shown: collisionless shocks and charging of small bodies immersed in a plasma.
Structure-preserving geometric particle-in-cell algorithm suppresses finite-grid instability -- Comment on "Finite grid instability and spectral fidelity of the electrostatic Particle-In-Cell algorithm'' by Huang et al
Comment on "Impact of particle number and cell-size in fully implicit charge- and energy-conserving particle-in-cell schemes" by N. Savard et al., Phys. Plasmas 32, 073903 (2025)
Los Alamos National Laboratory（洛斯阿拉莫斯国家实验室）；Lawrence Livermore National Laboratory（劳伦斯利弗莫尔国家实验室）
Quantitatively consistent computation of coherent and incoherent radiation in particle-in-cell codes - a general form factor formalism for macro-particles
Sparse Grids based Adaptive Noise Reduction strategy for Particle-In-Cell schemes
提出了一种基于稀疏网格的静电粒子模拟自适应降噪策略。我们的方法基于依赖于稀疏网格而不是规则网格的关键思想，以便在相同的粒子总数的情况下增加每个单元的粒子数量，如Ricketson和Cerfon（Plasma Phys. and Control. Fusion，59（2），024002）。采用一种新的过滤的角度来看，这一想法，我们构造的算法，使它可以很容易地集成到高性能的大规模PIC代码库。与PIC代码中通常使用的物理和傅立叶域滤波器不同，我们的方法自动适应网格大小，每个单元格的粒子数，密度分布的平滑度和初始采样技术。由于截断组合技术，我们可以减少较大的基于网格的误差的标准稀疏网格方法的非对齐和非光滑的功能。我们提出了一个启发式的形式误差分析的基础上选择最佳的截断参数在每个时间步，并开发了一个自然的框架，以尽量减少稀疏PIC模拟的总误差。我们证明了它的效率和性能通过两个测试用例：在二维的二极管不稳定性，和三维电子动力学的潘宁陷阱。我们的运行时性能的研究表明，我们的新方案可以提供显着的加速和内存减少相比，定期PIC实现可比的精度在电荷密度沉积。
Studying particle acceleration from driven magnetic reconnection at the termination shock of a relativistic striped wind using particle-in-cell simulations
