| 摘要: |
| 说明如何利用并行自适应有限元软件平台PHG 求解生物分子溶液体系的非线性Poisson-Boltzmann方程，并介绍一种解决这类问题的方法，它将网格生成与自适应计算过程结合在一起，可自动产生合适的网格，避免复杂的曲面网格生成步骤.之前的网格生成工作有：（1） TMSmesh生成高斯曲面的三角网格; （2） TransforMesh删除自相交的三角网格; （3） ISO2Mesh提高表面网格质量3个步骤.而基于PHG的自适应加密模块可以在逐次调整网格的同时保持动态负载平衡，高效地得到计算网格用于近似求解非线性Poisson-Boltzmann方程.计算了小球模型和AChE系统，分别从误差指示子下降阶和溶剂化能收敛的角度验证了方法的有效性，并且还将网格生成算法成功地应用于gA离子通道. |
| 关键词: 并行计算 有限元方法 自适应网格生成 非线性Poisson-Boltzmann 方程 |
| DOI： |
| 分类号: |
| 基金项目: |
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| Parallel Finite Element Algorithms and Adaptive Mesh Generation for Solving Nonlinear Poisson-Boltzmann Equations |
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XIE Yan, TU Bin, LU Ben-Zhuo, ZHANG Lin-Bo
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The State Key Laboratory of Scientific and Engineering Computing, Academy of Mathematics and Systems Science, The Chinese Academy of Sciences, Beijing 100190, China
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| Abstract: |
| This paper presents a parallel finite element algorithm based on the toolbox PHG for solving the nonlinear Poisson-Boltzmann equations for biomolecular systems. Previously TMSmesh, TransforMesh and ISO2Mesh were used to generate high resolution meshes. In this work a new method which combines mesh generation and adaptive mesh refinement is introduced to avoid complicated mesh generation steps. The new approach makes use of the capabilities of PHG in local mesh refinement and dynamic load balancing. The efficiency of the new method is demonstrated with a sphere model and the AChE system through both the decay of the a posteriori error estimates and the convergence of solvation-energy. In the meantime the method is also successfully applied to the Gramicidin Aion channel system. |
| Key words: parallel computing finite element method adaptive mesh generation non-linear Poisson-Boltzmann equation |
