一种使用加速笛卡尔展开快速计算周期势的O(N)方法
An O(N) Method for Rapidly Computing Periodic Potentials Using Accelerated Cartesian Expansions
AI总结：
提出一种基于加速笛卡尔展开（ACE）的O(N)方法，用于高效计算周期Helmholtz、Coulomb和Yukawa势，并验证了误差收敛和成本缩放。
摘要：
周期多体系统中长程势的评估是许多有趣物理问题数值建模的必要步骤。直接评估这些势需要O(N^2)次操作和O(N^2)存储，其中N是相互作用体的数量。在这项工作中，我们提出了一种需要O(N)次操作和O(N)存储的方法，用于评估在1维、2维和3维中具有周期性的周期Helmholtz、Coulomb和Yukawa势，该方法使用加速笛卡尔展开（ACE）。我们介绍了在ACE框架内实现这种加速所需的所有方面，包括必要的平移算子，以及适当修改分层计算算法。我们还展示了一些结果，验证了该方法在误差收敛和成本缩放方面的有效性，并推导了一个示例势的误差界。
英文摘要：
The evaluation of long-range potentials in periodic, many-body systems arises as a necessary step in the numerical modeling of a multitude of interesting physical problems. Direct evaluation of these potentials requires O(N^2) operations and O(N^2) storage, where N is the number of interacting bodies. In this work, we present a method, which requires O(N) operations and O(N) storage, for the evaluation of periodic Helmholtz, Coulomb, and Yukawa potentials with periodicity in 1-, 2-, and 3-dimensions, using the method of Accelerated Cartesian Expansions (ACE). We present all aspects necessary to effect this acceleration within the framework of ACE including the necessary translation operators, and appropriately modifying the hierarchical computational algorithm. We also present several results that validate the efficacy of this method with respect to both error convergence and cost scaling, and derive error bounds for one exemplary potential.
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