任意充满空间的Voronoi多面体泊松方程的精确和快速数值解：近场修正的再讨论
Accurate and fast numerical solution of Poisson's equation for arbitrary, space-filling Voronoi polyhedra: near-field corrections revisited
摘要：
本文提出了一种精确而快速地求解充满空间的、任意形状的凸Voronoi多面体（VP）的Poisson方程的方法，其时间复杂度为O（NVP），其中NVP是表示系统的不同VP的个数。实际上，我们解决了长期存在的问题，快速但准确的数值解的近场校正（NFC），贡献每个VP潜在的附近VP -通常涉及多极型条件收敛的总和，或快速傅立叶变换。我们的方法避免了所有的病态收敛和，是简单的，准确的，有效的，和工程一般，即，对于周期性固体、分子或具有无序或缺陷的系统。我们证明了该方法的实用性相比，精确可解模型的数值计算。
英文摘要：
We present an accurate and rapid solution of Poisson's equation for space-filling, arbitrarily- shaped, convex Voronoi polyhedra (VP); the method is O(NVP), where NVP is the number of distinct VP representing the system. In effect, we resolve the longstanding problem of fast but accurate numerical solution of the near-field corrections (NFC), contributions to each VP potential from nearby VP - typically involving multipole-type conditionally-convergent sums, or fast Fourier transforms. Our method avoids all ill-convergent sums, is simple, accurate, efficient, and works generally, i.e., for periodic solids, molecules, or systems with disorder or imperfections. We demonstrate the method's practicality by numerical calculations compared to exactly solvable models.
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