三维快速多极虚边界元配点法

Fast Multipole Virtual Boundary Element Collocation Method for Solving Three-dimensional Problems

以三维弹性力学问题为研究背景,提出了一种三维快速多极虚边界元配点法的求解思想,即将三维快速多极展开的基本思想和广义极小残值法运用于求解传统虚边界元配点法方程.文中将三维弹性问题的基本解推导为适合于虚边界元快速多极算法的展开格式,经数值计算格式的演变,使求解方程的计算量和储存量与所求问题的计算自由度数成线性比例,以达到数值模拟大规模自由度问题的目的.算例说明了该方法的可行性、计算效率和计算精度.此外,该方法的思想具有一般性,应用上具有扩展性.

In the research background of the three dimensional elasticity problem,the idea of the three-dimensional fast multipole virtual boundary element collocation method is proposed,in other words,the generalized minimal residual（GMRES） algorithm and the basic idea of fast multipole method（FMM） are jointly employed to solve the equations related to virtual boundary element collocation method（VBEM）.The fundamental solutions of three-dimensional problem of elasticity are derived as the numerical scheme to be suitable for the FMM of virtual boundary element method.After the evolution of numerical format,the amount of the computational elapsed time and the memory volume of the storage problems with the calculation of demand are linearly proportional to the number of degrees of freedom of the problem to be solved.Then the numerical simulation large-scale degrees of freedom question might be achieved by the method.The numerical examples have proved the feasibility,efficiency and calculating precision of the method.Moreover,the idea of the proposed method has the generality and the extension in the engineering applications.