论文标题
校正后的梯形规则 - 线性化泊松托尔兹曼方程
Corrected Trapezoidal Rule-IBIM for linearized Poisson-Boltzmann equation
论文作者
论文摘要
在本文中，我们求解了线性化的泊松托玻璃到托架方程，用于建模溶剂中大分子的电势。我们得出了一个校正后的梯形规则，其精度提高了线性化泊松托架方程的边界积分公式。更具体地说，与典型的边界积分配方相反，校正后的梯形规则被应用于使用$ \ Mathbb {r}^3 $中的均匀笛卡尔网格集成一个紧凑的支持的奇异积分系统，而无需显式表面参数化。通过快速多极方法加速的Krylov方法用于倒转产生的线性系统。我们研究了提出的方法的功效，并将其与现有的低阶方法进行比较。然后，我们将方法应用于浸入溶剂中的大分子的静电电位。由常用方法定义的溶剂排除表面仅是分段平滑的，我们研究了该方法对此类表面的有效性。
In this paper, we solve the linearized Poisson-Boltzmann equation, used to model the electric potential of macromolecules in a solvent. We derive a corrected trapezoidal rule with improved accuracy for a boundary integral formulation of the linearized Poisson-Boltzmann equation. More specifically, in contrast to the typical boundary integral formulations, the corrected trapezoidal rule is applied to integrate a system of compacted supported singular integrals using uniform Cartesian grids in $\mathbb{R}^3$, without explicit surface parameterization. A Krylov method, accelerated by a fast multipole method, is used to invert the resulting linear system. We study the efficacy of the proposed method, and compare it to an existing, lower order method. We then apply the method to the computation of electrostatic potential of macromolecules immersed in solvent. The solvent excluded surfaces, defined by a common approach, are merely piecewise smooth, and we study the effectiveness of the method for such surfaces.
