METHOD FOR THE POISSON-BOLTZMANN EQUATION

提出了一种快速并行边界元方法， 线性化Poisson方程的有效和鲁棒的数值解， 玻尔兹曼方程在生物分子静电场中的应用 离子强度效应很重要的问题。 在这样一个 分析，所有N个边界元素代表介质边界 在生物分子表面上彼此相互作用，因此包括 0（N2）存储和0（N3）CPU成本的多体问题， 传统的解决方法。 这两项成本都大幅降低， 0（N）的快速多极算法（FMAs）与一个有效的 迭代无矩阵求解程序。 所有快速BE分析的日期 一直局限于泊松方程的解（零离子 强度）。 因此，这里提出的关键技术进步是采用 FMA计算表面元素之间的Debye-Huckel相互作用 在整个盐浓度范围内。 充分利用 可用的计算资源，固有的并行的快速 开发BE分析软件，面向操作 在分布式系统上。 结果将同时显示 分析易处理的模型问题，也为代表 生物分子系统，以验证预期的计算性能 和准确性。 建议的商业应用 SBIR工作的成功完成，将使 政府、学术界和工业界提供先进的串行和并行快速 生物分子静电问题的BE软件 浸没在离子溶液中的组件。从使用中获得的知识 这种强大的计算工具在静电问题举行 有希望揭示静电相互作用对 生物过程并为基于结构的药物开辟新场所 设计

A fast parallel boundary element (BE) method is proposed for the efficient and robust numerical solution of the linearized Poisson- Boltzmann equation for application to biomolecular electrostatic problems where ionic strength effects are important. In such an analysis, all N boundary elements representing the dielectric boundary at the biomolecular surface interact with each other and thus comprise a many-body problem with 0(N2) storage and 0(N3) CPU costs in conventional solution methods. Both costs are drastically reduced to 0(N) by combining fast multipole algorithms (FMAs) with an efficient iterative matrix-free solution procedure. To date all fast BE analysis have been limited to the solution of the Poisson equation (zero ionic strength). Thus, a key technical advance proposed here is to employ a FMA to calculate the Debye-Huckel interactions between surface elements over the entire range of salt concentration. To make full use of available computational resources, the inherent parallelisum of the fast BE analysis will be exploited and the software oriented for operation upon distributed systems. Results will be presented for both analytically tractable model problems and also for representative biomolecular systems to verify the anticipated computational performance and accuracy. PROPOSED COMMERCIAL APPLICATION The successful completion of the SBIR effort, will make available to government, academia and industry an advanced serial and parallel fast BE software which will be used in electrostatic problems of biomolecular assemblies immersed in ionic solution. The knowledge gained from using such powerful computational tools in electrostatic problems hold the promises of revealing the effects of electrostatic interactions on biological processes and opening new venues for structure-based drug design.