An iterative PPPM method for simulating Coulombic systems on distributed memory parallel computers
An iterative PPPM method for simulating Coulombic systems on distributed memory parallel computers
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DOI：
10.1080/08927029808022044
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发表时间：
1998-01-01
影响因子：
2.1
通讯作者：
De Leeuw, SW
中科院分区：
文献类型：
--
作者：
Beckers, JVL;Lowe, CP;De Leeuw, SW
我们描述了从一个新的实施霍克尼的粒子网格（PPPM）的库仑能量和带电粒子的模拟力的评估方法获得的结果。而不是采取通常的方法，解决泊松方程的傅立叶变换的手段，我们使用迭代泊松求解器。在分子动力学（MD）模拟中，来自前一时间步的解为下一解提供了良好的起点。这将每个时间步的迭代次数减少到可接受的值。迭代方案的复杂度为O（N），与基于傅立叶变换的方法相比，它可以在并行结构上以最小的通信开销实现，我们研究了算法中误差的来源，发现通过使电荷密度分布尽可能平滑，可以最好地获得库仑相互作用的合理精度。这涉及将粒子电荷散布在大量网格点上。消除这些费用然后成为算法中最耗时的部分。我们展示了如何，然后我们可以获得相当大的节省计算时间采用扩散方程作为一个电荷传播mechanism.The效果采用的算法的准确性小于通常容忍的埃瓦尔德求和研究计算，从MD模拟二氧化硅，数量是敏感的库仑相互作用的长程部分。这些结果进行比较，充分埃瓦尔德和参考模拟，并发现在统计误差。
We describe results obtained from a new implementation of Hockney's Particle-Particle Particle-Mesh (PPPM) method for evaluation of Coulomb energies and forces in simulations of charged particles. Rather than taking the usual approach, solving Poisson's equation by means of a Fourier transformation, we use an iterative Poisson solver. In a molecular dynamics (MD) simulation the solution from the previous time-step provides a good starting point for the next solution. This reduces the number of iterations per time-step to acceptable values. The iterative scheme has a complexity O(N), and, in contrast with the Fourier transform based approach, it is easily implemented on a parallel architecture with a minimum of communication overhead.We examine the origin of the errors in the algorithm and find that reasonable accuracies in the Coulomb interaction can best be attained by making the charge density profile as smooth as possible. This involves spreading the particle charges over a large number of grid points. Assigning these charges then becomes the most time consuming part of the algorithm. We show how we can then gain a considerable saving in computing time by employing a diffusion equation as a charge spreading mechanism.The effect of employing the algorithm with an accuracy less than that typically tolerated in an Ewald summation is studied by computing, from an MD simulation of silica, quantities that are sensitive to the long range part of the Coulomb interaction. These results are compared to full Ewald sum reference simulations and found to be within the statistical error.