数值计算与计算机应用
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数值计算与计算机应用  2018, Vol. 39 Issue (2): 91-110    DOI:
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一种泊松-玻尔兹曼方程稳定算法的高效有限元并行实现
邓维山1,2, 徐进1
1. 中国科学院软件研究所, 北京 100190;
2. 中国科学院软件研究所, 北京 100190
AN EFFECTIVE PARALLEL IMPLEMENTED FOR AN STABLE METHOD OF POISSON-BOLTZMANN EQUATION BASED ON FINITE ELEMENT METHOD
Deng Weishan1,2, Xu Jin1
1. Institute of Software, Chinese Academy of Sciences, Beijing 100190, China;
2. University of Chinese Academy of Sciences, Beijing 100049, China
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摘要 泊松-玻尔兹曼方程(Poisson-Boltzmann Equation,PBE)是广泛应用于溶剂化生物分子静电分析的隐式溶剂化模型.本文在原有有限元软件基础上对近来提出的基于高阶有限元求解PBE的无条件稳定方法[9]设计并实现了一种高效的并行计算方法.无条件稳定方法对PBE拟时间迭代求解,避开了强非线性导致的不稳定性.基于非结构化四面体网格本文设计实现了基于代数分解的求解稀疏线性方程组的高效并行模型.规模可扩展至6400 CPU核,并行效率达到近86%.大规模并行迭代求解线性方程组是计算科学领域的共性问题,它的高效并行实现不仅对实际生物分子静电分析提供了很好的基础,也可扩展至其他各应用领域.
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关键词并行计算   线性方程组   泊松-玻尔兹曼方程   有限元方法   拟时间方法     
Abstract: The Poisson-Boltzmann Equation (PBE) is a widely used implicit solvent model for the electrostatic analysis of solvated biomolecules. An effective parallel algorithm has been implemented to an unconditional stable method of PBE based on high-order Finite Element Method (FEM). The unconditional stable method takes a pseudo-time approach to address the exponential nonlinearity of the PBE, which completely suppresses the nonlinear instability. Based on unstructured tetrahedral mesh, an effective parallel model has been designed for the linear algebra system based on algebraic decomposition. A nearly ideal weak-scaling efficiency of 86% has been achieved on 6400 CPU cores. This effective linear algebraic solver builds a strong foundation to simulation of biomolecular electrostatics. What's more, it can be applied to numerous real scientific applications.
Key wordsparallel computing   algebra system   poisson-boltzmann equation   finite element method   pseudo-time approach   
收稿日期: 2017-04-28;
引用本文:   
. 一种泊松-玻尔兹曼方程稳定算法的高效有限元并行实现[J]. 数值计算与计算机应用, 2018, 39(2): 91-110.
. AN EFFECTIVE PARALLEL IMPLEMENTED FOR AN STABLE METHOD OF POISSON-BOLTZMANN EQUATION BASED ON FINITE ELEMENT METHOD[J]. Journal of Numerical Methods and Computer Applicat, 2018, 39(2): 91-110.
 
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