A new algorithm for charge deposition for multiple-grid method for PIC simulations in r-z cylindrical coordinates
A new algorithm for charge deposition for multiple-grid method for PIC simulations in r-z cylindrical coordinates
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DOI：
10.1016/j.jcp.2007.01.004
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发表时间：
2007-07
期刊：
影响因子：
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通讯作者：
C. Cornet;D. Kwok
中科院分区：
文献类型：
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作者：
C. Cornet;D. Kwok
可以在某些区域中细化在粒子-单元模拟中使用的节点的网格，以获得更好的局部空间分辨率，而不增加过多的计算成本。每一次细化都可以看作是多重网格系统中的一个更精细的网格。详细介绍了二维柱坐标系下多重网格系统的标准双线性加权法，指出了该方法的不足之处。一个新的算法的粒子到节点的加权在多重网格系统，然后描述和比较标准的双线性加权方法在二维（r-z）柱坐标。本说明特别注意不同单元格大小的网格之间的界面附近的节点。本研究中使用的体积加权方法在几何上类似于笛卡尔坐标中的标准双线性PIC方法，但权重与z轴周围区域的旋转体积成比例，而不是区域本身。由于体积加权法具有内置的轴对称几何形状，因此在这种特定情况下使用它是一种自然的系统。采用0.5×0.5，1×1和2× 2 mm三种网格，对平板平台金属等离子体浸没离子注入和沉积（MePIIID）进行了粒子模拟，并与相同参数下的单网格模拟结果进行了比较。多重网格方法与单网格模拟相比非常好。
A mesh of nodes used in particle-in-cell simulations may be refined in some regions to obtain better local spatial resolution without adding excessive computational cost. Each refinement can be seen as a finer grid in a multiple-grid system. The standard bilinear weighting method in two-dimensional (r–z) cylindrical coordinates using a multiple-grid system is detailed and an inadequacy in the method is presented. A new algorithm of particle to node weighting in a multiple-grid system is then described and compared to the standard bilinear weighting method in two-dimensional (r–z) cylindrical coordinates. This description pays particular attention to the nodes near the interface between grids of differing cell-size. The volume weighting method used in this study is geometrically similar to the standard bilinear PIC method in Cartesian coordinates, but weights in proportion to the volumes of revolution of the areas about the z-axis, rather than the areas themselves. As the volume weighting method has the axisymmetric geometry built in, it is a natural system to use in this particular case. A full particle-in-cell (PIC) simulation of metal plasma-immersion ion implantation and deposition (MePIIID) of a flat stage using three grids of cell size: 0.5×0.5, 1×1 and 2×2mm; is performed and results are compared to those obtained from a single-grid simulation with the same parameters. The multiple grid method compares very well to the single-grid simulation.