Lu Benzhuo, McCammon J Andrew
Howard Hughes Medical Institute, Center for Theoretical Biological Physics, Department of Chemistry and Biochemistry, and Department of Pharmacology, University of California at San Diego, La Jolla, California 92093-0365.
J Chem Theory Comput. 2007 May;3(3):1134-42. doi: 10.1021/ct700001x.
A patch representation differing from the traditional treatments in the boundary element method (BEM) is presented, which we call the constant "node patch" method. Its application to solving the Poisson-Boltzmann equation (PBE) demonstrates considerable improvement in speed compared with the constant element and linear element methods. In addition, for the node-based BEMs, we propose an efficient interpolation method for the calculation of the electrostatic stress tensor and PB force on the solvated molecular surface. This force calculation is simply an O(N) algorithm (N is the number of elements). Moreover, our calculations also show that the geometric factor correction in the boundary integral equations significantly increases the accuracy of the potential solution on the boundary, and thereby the PB force calculation.
提出了一种与边界元法（BEM）中传统处理方法不同的面片表示法，我们称之为常数“节点面片”法。将其应用于求解泊松-玻尔兹曼方程（PBE），结果表明与常数单元法和线性单元法相比，速度有显著提高。此外，对于基于节点的边界元法，我们提出了一种高效的插值方法，用于计算溶剂化分子表面上的静电应力张量和PB力。这种力的计算仅仅是一种O(N)算法（N是单元数量）。而且，我们的计算还表明，边界积分方程中的几何因子校正显著提高了边界上电势解的精度，从而提高了PB力的计算精度。
