非重叠Mortar有限元法及其并行计算在静电场问题中的应用  

Application of Non-overlapping Mortar Finite Element Method and Parallel Computing in Electrostatic Problems

作　　者：王栋[1] 阮江军[1] 彭迎[2] 刘守豹[1] 杜志叶[1] 黄道春[1] 

机构地区：[1]武汉大学电气工程学院,湖北省武汉市430072 [2]湖北省电力公司,湖北省武汉市430077

出　　处：《中国电机工程学报》2012年第15期162-169,1,共8页Proceedings of the CSEE

基　　金：国家自然科学基金项目(50977066)~~

摘　　要：采用Mortar有限单元法(mortar finite element method,MFEM)能够得到正定、对称的系数矩阵,而且刚度矩阵是分块对称的,这种特点适合于并行迭代求解。阐述了非重叠Mortar有限单元法(non-overlapping MFEM,NO-MFEM)的基本原理,介绍了适合于NO-MFEM并行计算的区域分解策略以及并行求解的基本流程。针对简单2维静电场问题,使用NO-MFEM进行了并行计算,并与理论值和串行计算结果进行对比,验证了所提方法的有效性。同时,对于非协调网格造成的计算误差进行了分析。NO-MFEM法的并行计算为工程应用中优化设计问题的区域分解和并行求解提供了一种新的选择。Mortar finite element method （MFEM） can obtain a positive definite, symmetric coefficient matrix which is block symmetric. This method based on nonconforming finite element. These features are suitable for parallel iterative computing. This paper gives the fundamental of non-overlapping MFEM （NO-MFEM）; the domain decomposition strategy is introduced which is convenient for NO-MFEM parallel computing; the procedures of parallel computing are discussed. By two dimensional electrostatic models, the validity of NO-MFEM parallel computing was proved. The results of parallel computing are similar to the results of serial computing and the theoretical value. Moreover, the calculation error caused by the nonconforming grid is analyzed. This work is fundamental for extending MFEM to optimization design and other applications in computational electromagnetics.

关 键 词：非重叠Mortar有限元法 并行计算 区域分解 连续条件 静电场 优化设计 

分 类 号：TM15[电气工程—电工理论与新技术]