基于非局域电荷转移的静电问题数值解法--罗宾汉法
The Robin Hood method - a novel numerical method for electrostatic problems based on a non-local charge transfer
摘要：
我们介绍一种新的数值方法，命名为罗宾汉方法，解决静电问题。该方法的方法是最接近的边界元法，虽然这类方法存在显着的概念差异。该方法通过迭代的非局域电荷转移实现了导电表面的等电位。对于每个导电表面，在与表面的目标等势性差异最大的表面元素之间执行非局部电荷转移。该方法进行了测试，对分析解决方案，其广泛的应用范围被证明。该方法具有吸引人的技术特点。对于具有N个表面元素的问题，该方法的计算复杂度基本上与N^alpha成比例，其中alpha < 2，所需的计算机存储器与N成比例，而对于误差的许多数量级，势的误差随着迭代次数呈指数下降，而不存在临界减速。罗宾汉方法在其他经典和量子问题中有很大的应用潜力。概述了静电学之外的一些可能的应用。
英文摘要：
We introduce a novel numerical method, named the Robin Hood method, of solving electrostatic problems. The approach of the method is closest to the boundary element methods, although significant conceptual differences exist with respect to this class of methods. The method achieves equipotentiality of conducting surfaces by iterative non-local charge transfer. For each of the conducting surfaces non-local charge transfers are performed between surface elements which differ the most from the targeted equipotentiality of the surface. The method is tested against analytical solutions and its wide range of application is demonstrated. The method has appealing technical characteristics. For the problem with N surface elements, the computational complexity of the method essentially scales with N^alpha, where alpha < 2, the required computer memory scales with N, while the error of the potential decreases exponentially with the number of iterations for many orders of magnitude of the error, without the presence of the Critical Slowing Down. The Robin Hood method has a large potential of application in other classical as well as quantum problems. Some possible applications outside electrostatics are outlined.
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