Multilevel Summation for the Fast Evaluation of Forces for the Simulation of Biomolecules
Multilevel Summation for the Fast Evaluation of Forces for the Simulation of Biomolecules
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发表时间：
2006
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通讯作者：
David J. Hardy
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作者：
David J. Hardy
多级求和方法计算成对静电相互作用势和各自力的近似值。标量势被平滑地分成精确计算的短程部分和从网格层次结构近似的缓慢变化的长程部分。多级求和特别适合生物分子的动态模拟，因为它计算作为标量势的梯度的连续力。它提供了一种统一的静电计算方法，其中相同的方法可用于周期性和非周期性边界条件，其工作量随着系统的大小线性缩放。多级求和也足够灵活，可以应用于其他成对势。本论文提供了迄今为止对多级求和方法及其在计算静电相互作用中的应用的最彻底的研究。数学和算法细节与精确的操作计数一起呈现。分析了该方法的近似误差，并根据基本方法参数制定了误差范围。成本和误差分析能够确定最佳方法参数以获得所需的误差容限。考虑了各种近似插值方案，并检查了几种平滑静电势的替代方法。讨论了该方法在不同边界条件下的使用，结果表明，将多级求和应用于周期性势会产生有限和，截断表示为有界逼近误差。多级求和的性能被证明优于其他常用的静电快速方法，同时提供了相当的精度。该方法还被证明可以产生稳定的动态，从而实现更便宜、精度更低的近似。
The multilevel summation method computes an approximation to the pairwise electrostatic interaction potential and respective forces. The scalar potential is smoothly split into a short-range part computed exactly and a slowly varying long-range part approximated from a hierarchy of grids. Multilevel summation is especially appropriate for the dynamical simulation of biomolecules, because it computes continuous forces that are the gradient of a scalar potential. It provides a unified approach to computing electrostatics, in which the same method can be used for periodic and nonperiodic boundary conditions, with an amount of work that scales linearly as the size of the system. Multilevel summation is also flexible enough to be applied to other pairwise potentials. This thesis provides the most thorough investigation to date of the multilevel summation method and its use for computing electrostatic interactions. The mathematical and algorithmic details are presented along with a precise operation count. The approximation error from the method is analyzed, with error bounds formulated in terms of the fundamental method parameters. The cost and error analyses enable the determination of optimal method parameters for a desired error tolerance. Various interpolation schemes for the approximation are considered, and several alternative approaches to smoothing the electrostatic potential are examined. The use of the method with different boundary conditions is discussed, and it is shown that the application of multilevel summation to the periodic potential yields a finite sum, with the truncation expressed as bounded approximation error. The performance of multilevel summation is demonstrated to be superior to other commonly used fast methods for electrostatics, while providing comparable accuracy. The method is also shown to produce stable dynamics for cheaper, lower accuracy approximation.