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首页> 外文期刊>The Journal of Chemical Physics >Harmonic surface mapping algorithm for fast electrostatic sums
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Harmonic surface mapping algorithm for fast electrostatic sums

机译：快速静电和谐波表面映射算法

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摘要

We propose a harmonic surface mapping algorithm (HSMA) for electrostatic pairwise sums of an infinite number of image charges. The images are induced by point sources within a box due to a specific boundary condition which can be non-periodic. The HSMA first introduces an auxiliary surface such that the contribution of images outside the surface can be approximated by the least-squares method using spherical harmonics as basis functions. The so-called harmonic surface mapping is the procedure to transform the approximate solution into a surface charge and a surface dipole over the auxiliary surface, which becomes point images by using numerical integration. The mapping procedure is independent of the number of the sources and is considered to have a low complexity. The electrostatic interactions are then among those charges within the surface and at the integration points, which are all the forms of Coulomb potential and can be accelerated straightforwardly by the fast multipole method to achieve linear scaling. Numerical calculations of the Madelung constant of a crystalline lattice, electrostatic energy of ions in a metallic cavity, and the time performance for large-scale systems show that the HSMA is accurate and fast, and thus is attractive for many applications. Published by AIP Publishing.
机译：我们提出了一种谐波表面映射算法（HSMA），用于无限数量的图像电荷的静电成对和。由于可以是非周期性的特定边界条件，由框内的点源引起图像。 HSMA首先引入辅助表面，使得表面外部的图像的贡献可以通过使用球面谐波作为基函数的最小二乘法来近似。所谓的谐波表面映射是将近似解变成表面电荷和辅助表面上的表面偶极子的过程，其通过使用数值积分而变为点图像。映射过程与源的数量无关，并且被认为具有低复杂性。然后，静电相互作用在表面内的那些电荷和整体点，这是Coulomb电位的所有形式，并且可以通过快速的多极方法直接加速以实现线性缩放。金属腔中的晶格Madelung常数的数值计算，金属腔中的离子静电能，以及大规模系统的时间性能表明，HSMA是准确且快速的，因此对许多应用具有吸引力。通过AIP发布发布。

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