An efficient algorithm for classical density functional theory in three dimensions: ionic solutions.
An efficient algorithm for classical density functional theory in three dimensions: ionic solutions.
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DOI：
10.1063/1.3357981
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发表时间：
2009-10
期刊：
影响因子：
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通讯作者：
M. Knepley;D. Karpeev;S. Davidovits;R. Eisenberg;D. Gillespie
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文献类型：
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作者：
M. Knepley;D. Karpeev;S. Davidovits;R. Eisenberg;D. Gillespie
流体的经典密度泛函理论 (DFT) 是分析非均匀流体的重要工具。然而，三维系统的数值求解算法很少。在这里，我们提出了一种针对带电硬球流体的有效数值方案，该方案使用 O(N log N) 运算和 O(N) 内存，其中 N 是网格点的数量。由于三维系统需要非常大的 N，因此系统规模的缩放非常重要。该算法使用快速傅立叶变换 (FFT) 来评估 DFT 欧拉-拉格朗日方程的卷积，并使用皮卡德（迭代替换）迭代和线搜索来求解方程。这种 FFT/Picard 技术的优缺点与使用卷积的实空间积分而不是 FFT 和牛顿迭代而不是 Picard 的替代解决方法进行了比较。对于硬球 DFT，我们使用基本测度论。对于静电 DFT，我们提出了两种算法。一种是罗森菲尔德的“散装流体”泛函 [Y.罗森菲尔德，J.化学。物理。 98, 8126 (1993)] 使用 O(N log N) 运算。另一个是“参考流体密度”(RFD) 函数 [D. Gillespie 等人，J. Phys.：Condens。事项 14, 12129 (2002)]。该函数比散装流体函数准确得多，但 RFD 算法需要 O(N(2)) 运算。
Classical density functional theory (DFT) of fluids is a valuable tool to analyze inhomogeneous fluids. However, few numerical solution algorithms for three-dimensional systems exist. Here we present an efficient numerical scheme for fluids of charged, hard spheres that uses O(N log N) operations and O(N) memory, where N is the number of grid points. This system-size scaling is significant because of the very large N required for three-dimensional systems. The algorithm uses fast Fourier transforms (FFTs) to evaluate the convolutions of the DFT Euler-Lagrange equations and Picard (iterative substitution) iteration with line search to solve the equations. The pros and cons of this FFT/Picard technique are compared to those of alternative solution methods that use real-space integration of the convolutions instead of FFTs and Newton iteration instead of Picard. For the hard-sphere DFT, we use fundamental measure theory. For the electrostatic DFT, we present two algorithms. One is for the "bulk-fluid" functional of Rosenfeld [Y. Rosenfeld, J. Chem. Phys. 98, 8126 (1993)] that uses O(N log N) operations. The other is for the "reference fluid density" (RFD) functional [D. Gillespie et al., J. Phys.: Condens. Matter 14, 12129 (2002)]. This functional is significantly more accurate than the bulk-fluid functional, but the RFD algorithm requires O(N(2)) operations.