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Application of fast multipole Galerkin boundary integral equation method to elastostatic crack problems in 3D

机译:快速多极Galerkin边界积分方程方法在3D弹力裂纹问题中的应用

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摘要

Fast multipole method (FMM) has been developed as a technique to reduce the computational cost and memory requirements in solving large-scale problems. This paper discusses an application of FMM to three-dimensional boundary integral equation method for elastostatic crack problems. The boundary integral equation for many crack problems is discretized with FMM and Galerkin's method. The resulting algebraic equation is solved with generalized minimum residual method (GMRES). The numerical results show that FMM is more efficient than conventional methods when the number of unknowns is more than about 1200 and, therefore, can be useful in large-scale analyses of fracture mechanics.
机译:快速多极方法(FMM)已被开发为一种在解决大规模问题时降低计算成本和内存需求的技术。本文讨论了FMM在弹性边界问题三维边界积分方程法中的应用。用FMM和Galerkin方法离散了许多裂纹问题的边界积分方程。所得的代数方程式用广义最小残差法(GMRES)求解。数值结果表明,当未知数大于1200时,FMM比常规方法更有效,因此可用于大规模的断裂力学分析。

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