位势问题Trefftz有限元法的研究进展  

Research Advances in Trefftz Finite Element Method for Potential Problems

作　　者：王克用[1] 岑皓[2] 李培超[1] WANG Keyong CEN Hao LI Peichao(School of Mechanical Engineering, Shanghai University of Engineering Science, Shanghai 201620, China Office of Campus Construction, Tianjin Foreign Studies University, Tianjin 300204, China)

机构地区：[1]上海工程技术大学机械工程学院,上海201620 [2]天津外国语大学基建处,天津300204

出　　处：《上海工程技术大学学报》2017年第3期204-209,共6页Journal of Shanghai University of Engineering Science

摘　　要：简述Trefftz有限元法在位势问题中的研究进展,分析单元域内插值函数以及杂交泛函的构造方法.该构造方法使Trefftz有限元法具有诸多优点,如对网格畸变不敏感,多边形单元构造便捷,单元公式只涉及边界积分以及局部效应处理高效.文末,展望了该领域未来的两个发展方向.Research advances in the Trefftz finite element method were reviewed for potential problems. The construction procedure was investigated for the intra-element interpolation functions as well as the hybrid functional. It is found that this construction approach makes the Trefftz finite element method possess many advantages such as insensitivity to mesh distortion, easy construction of polygonal elements, element formulation involving boundary integrations only and treatment of local effects with high efficiency. In the end,two prospectives in the field were proposed for future developments.

关 键 词：位势问题 Trefftz有限元法 杂交泛函 Trefftz函数 

分 类 号：O241[理学—计算数学]