摘要
对于复杂的非线性工程问题的数值模拟,边界元法(BEM)日益显示出优于区域解法的长处,特别是时间相关(需按时段逐步迭代推进)和含各种不定边界(造成可变区域,网络需不断重分)的情形,BEM可显著减少存贮要求与计算量.针对非线性问题数值模拟的主要难点,即微分算子线性化,时间相关项与可动边界(非线性边条)的处理等,综述了国内外边界无法学术界的近期研究进展,总体目标是寻求一种适应多种微分算子、非线性迭代和时段推进计算效能高的稳定数值模式.
For the numerical modelling of complicated nonlinear problems, BEM model shows to be superior to the domain solution methods. Especially, for time-dependent problem (for which a time-marching scheme is needed) and for moving boundary (which means changeable solution domain and boundary where the regeneration of network is needed), BEM could reduce the storage requirement and CPU time considerably. In this paper, some principal difficulties, such as the linearization of the differential operator, the treatment of time-dependence and moving boundary are discussed including some novel ideas in literature. The main purpose is to establish an efficient and stable numerical model for time marching and nonlinear iteration suitable to a variety of differential equations.
出处
《力学进展》
EI
CSCD
北大核心
2000年第1期47-54,共8页
Advances in Mechanics
基金
国家自然科学基金!19772036
关键词
非线性边界元
非定常不定边界问题
力学
nonlinear BEM, linearization of differential equations, transient moving boundaries, analytical treatment of volume integral