快速多极多域虚边界元法解不同材料组合结构

Fast Multipole Multi-domain VBEM for Solving the Composite Structures of Different Materials

将快速多极算法和广义极小残值法(GMRES)的基本思想运用于虚边界元法的方程求解中,并构造了多域组合问题虚边界元法的快速多极展开的实施思路,且将此方法用于不同材料组合结构问题的求解.采用此方法能够使得原问题方程组求解的计算耗时量和储存量降至与所求问题的计算自由度数成线性比例.数值算例验证了方法的可行性、计算精度和计算效率.

The main theory of generalized minimal residual algorithm （GMRES） and fast multipole method （FMM） are applied into the numerical solution of equations about virtual boundary element method （VBEM） to form the idea about the fast multipole expansion of multi-domain VBEM, which is applied to solve the composite structures of different materials. With the method, 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. Numerical examples are presented to demonstrate the feasibility, accuracy and efficiency of the method.