Fast multipole boundary element methods (FMBEMs) are developed based on the couple of fast multipole algorithm and generalized minimal residual algorithm. The FMBEMs improve the efficiency of conventional BEMs, accelerate the computing, enlarge the solving scale, and it is applied in various engineering fields. The paper tried to do a brief review for the FMBEMs, and focus on the description of basic principles and applications in rolling engineering. The basic principles and main frameworks of two typical methods of FMBEMs (sphere harmonic function multipole BEM and Taylor series multipole BEM) are briefly described, and then the key numerical iterative and preconditioning techniques suitable for the FMBEMs are introduced. The typical numerical examples are presented, including the elasticity problems, the elastic contact problems and the elastoplasticity problems, etc. The validity and effectiveness of FMBEMs are effectively illustrated by engineering analysis examples. The numerical results suggest that the FMBEMs are suitable for the analysis and solution of large scale rolling engineering problems. The implementation process of numerical analysis can provide useful reference for the applications in other engineering fields.
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