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| 1 | 并行自适应有限元软件平台PHG及其应用显示文摘PHG(parallel hierarchical grid)是一个由中国科学院'科学与工程计算国家重点实验室'研制的开源并行自适应有限元程序开发平台.与国际上其他同类型软件相比,其主要特征有:(1)提供基于最新顶点单元二分的非结构协调四面体网格并行局部加密;(2)支持h-p自适应有限元计算;(3)支持大规模并行和动态负载平衡;(4)提供大型稀疏线性方程组直接求解和灵活的预处理迭代求解.本文介绍PHG平台的主要模块和核心算法,以及基于PHG平台开发的一些并行有限元应用程序,它们包括:大型变压器铁损模拟、离子通道中的离子输运过程模拟、集成电路互连线寄生参数提取、冰盖模拟、弹性波PML方程谱元计算等. | 张林波 郑伟英 卢本卓 崔涛 冷伟 林灯 | 2016 | 中国科学:信息科学2016，46，10： | 10 |
| 2 | 基于三维自适应有限元的阀厅全模型电场分布并行计算显示文摘大规模复杂模型电磁场数值仿真问题一直是计算电磁学中比较难处理的问题。本文采用三维自适应有限元并行求解算法处理此类问题,以某±660kV换流站阀厅全模型电场模拟为例,对阀厅内部关注区域金具表面电场进行仿真计算。并行计算结果与串行计算结果相吻合,验证了本文提出的并行求解算法的正确性和可行性。该并行求解算法,可以显著提高求解速度,实现对于大规模复杂电磁问题的高效数值模拟。 | 王栋 阮江军 杜志叶 谢伟 蒲兵舰 | 2014 | 现代电力2014，31，6： | 3 |
| 3 | 并行自适应有限元计算中的负载平衡研究显示文摘偏微分方程的并行求解,关键问题之一是网格划分,它不仅要求每个进程拥有相等的计算负载,同时要求有良好的划分质量,以减少进程间通信.在自适应有限元计算过程中,网格/基函数不断调整,会导致负载不平衡,必须动态地调整网格分布,从而实现动态负载平衡.本文研究了不同的负载平衡方法,并在并行自适应有限元平台PHG中实现.数值实验表明我们的动态负载平衡算法具有很高的划分质量,运行速度快,可有效划分网格并减少运行时间. | 刘辉 冷伟 崔涛 | 2015 | 数值计算与计算机应用2015，36，3： | 2 |
| 4 | WELL-CONDITIONED FRAMES FOR HIGH ORDER FINITE ELEMENT METHODS显示文摘The purpose of this paper is to discuss representations of high order C^(0)finite element spaces on simplicial meshes in any dimension.When computing with high order piecewise polynomials the conditioning of the basis is likely to be important.The main result of this paper is a construction of representations by frames such that the associated L^(2)condition number is bounded independently of the polynomial degree.To our knowledge,such a representation has not been presented earlier.The main tools we will use for the construction is the bubble transform,introduced previously in[1],and properties of Jacobi polynomials on simplexes in higher dimensions.We also include a brief discussion of preconditioned iterative methods for the finite element systems in the setting of representations by frames. | Kaibo Hu Ragnar Winther | 2021 | Journal of Computational Mathematics2021，39，3： | 0 |
| 5 | UNCONDITIONAL CONVERGENCE AND ERROR ESTIMATES OF A FULLY DISCRETE FINITE ELEMENT METHOD FOR THE MICROPOLAR NAVIER-STOKES EQUATIONS显示文摘In this paper,we consider the initial-boundary value problem(IBVP)for the micropolar Naviers-Stokes equations(MNSE)and analyze a first order fully discrete mixed finite element scheme.We first establish some regularity results for the solution of MNSE,which seem to be not available in the literature.Next,we study a semi-implicit time-discrete scheme for the MNSE and prove L2-H1 error estimates for the time discrete solution.Furthermore,certain regularity results for the time discrete solution are establishes rigorously.Based on these regularity results,we prove the unconditional L2-H1 error estimates for the finite element solution of MNSE.Finally,some numerical examples are carried out to demonstrate both accuracy and efficiency of the fully discrete finite element scheme. | Shipeng Mao Jiaao Sun Wendong Xue | 2024 | Journal of Computational Mathematics2024，42，1： | 0 |
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