摘要
针对快速多极虚边界元法是将快速多极展开算法和广义极小残值法(GMRES)引入虚边界元法中的形成特点,采用了"源点"多极展开和"场点"局部展开的组合处理方案,形成快速多极虚边界方法,从而使得原问题方程组求解的计算耗时量和储存量均降至与所求问题的计算自由度数成线性比例。文中提供的高层剪力墙结构,应用快速多极虚边界元法对其进行了数值分析实例,目的是验证所提方法在普通个人微机上可计算百万以上计算自由度和对复杂剪力墙结构的分析能力。结果表明,快速多极虚边界元法能够在现有个人微机硬件条件下模拟大规模复杂问题,易于在工程实际中推广应用。数值算例验证了本方法的可行性、计算精度和计算效率。
The method-fast multipole virtual boundary element method （VBEM） is formed by introducing the generalized minimal residual algorithm （GMRES） and fast multipole method （FMM） to the VBEM. Owing to the combined scheme of multipole expansion at the collocation point and local expansion at the integration point, the complexities of operation and memory about solution of the equations would be made to be of linear proportion to the freedoms of the problem. An example of tall shearwall structure is provided and simulated with the method in this paper, and the aim is to verify the capacity for analyzing complex shearwall structures with millions of freedoms on a laptop computer. Result show that the large scale complex problem can be solved with fast multipole VBEM under the current personal computer hardware condition, and it can be extended in engineering application. Numerical examples are presented to demonstrate the feasibility, accuracy and efficiency of the method.
出处
《结构工程师》
2008年第4期25-30,共6页
Structural Engineers
关键词
快速多极算法
广义极小残值法
虚边界元法
高层剪力墙结构
fast multipole method （FMM）, generalized minimal residual algorithm （GMRES）, virtual boundary element method （VBEM）, tall shearwall structure
