基于EBE-PCG(element by element-preconditioned conjugate gradient)策略的并行算法不用形成总体刚度矩阵,而且无需进行三维模型的区域分解,从而提高了并行计算的速度和效率,是实现协同优化设计的性能函数快速分析技术的有效途径。文...基于EBE-PCG(element by element-preconditioned conjugate gradient)策略的并行算法不用形成总体刚度矩阵,而且无需进行三维模型的区域分解,从而提高了并行计算的速度和效率,是实现协同优化设计的性能函数快速分析技术的有效途径。文中详细介绍有限元EBE(element by element)的运算方法,给出EBE-PCG并行算法的实现步骤,最后在网络集群环境下,综合运用多种编程语言和分析工具,实现基于EBE-PCG策略的三维有限元并行计算。计算结果表明,该并行算法的计算误差小,并行效率高,适合于性能函数的快速求解。展开更多
PCG2 （Preconditioned Conjugate-Gradient Method 2）, the most popular mothod used in groundwater field, was used to solve the distributed model of large-scale groundwater system. Its principle and effect was analyzed ...PCG2 （Preconditioned Conjugate-Gradient Method 2）, the most popular mothod used in groundwater field, was used to solve the distributed model of large-scale groundwater system. Its principle and effect was analyzed mathematically, and verified by some specific examples. Numerical results acquired by PCG2 are accurate, it demonstrates that PCG2 is effective on methodology itself and man-ralated operation. So PCG2 is worthy of popularizing in the area of groundwater system for numerical analysis.展开更多
文摘近日,西安电子科技大学数学与交叉科学研究院菁英副教授李哲与上海交通大学教授邢朝平、博士研究生姚逸洲和副教授袁晨合作,在伪随机关联生成器(Pseudorandom Correlation Generator,PCG)方面取得重要进展,相关论文“Efficient Pseudorandom Correlation Generators for Any Finite Field”被EUROCRYPT(欧密会)2025录用发表。
文摘基于EBE-PCG(element by element-preconditioned conjugate gradient)策略的并行算法不用形成总体刚度矩阵,而且无需进行三维模型的区域分解,从而提高了并行计算的速度和效率,是实现协同优化设计的性能函数快速分析技术的有效途径。文中详细介绍有限元EBE(element by element)的运算方法,给出EBE-PCG并行算法的实现步骤,最后在网络集群环境下,综合运用多种编程语言和分析工具,实现基于EBE-PCG策略的三维有限元并行计算。计算结果表明,该并行算法的计算误差小,并行效率高,适合于性能函数的快速求解。
基金Supported by National Natural Science Foundation (30370825)
文摘PCG2 （Preconditioned Conjugate-Gradient Method 2）, the most popular mothod used in groundwater field, was used to solve the distributed model of large-scale groundwater system. Its principle and effect was analyzed mathematically, and verified by some specific examples. Numerical results acquired by PCG2 are accurate, it demonstrates that PCG2 is effective on methodology itself and man-ralated operation. So PCG2 is worthy of popularizing in the area of groundwater system for numerical analysis.
