GMRES: a generalized minimal residual algorithm for solving nonsymmetric linear systems
SIAM Journal on Scientific and Statistical Computing
A fast algorithm for particle simulations
Journal of Computational Physics
Finite Elements in Analysis and Design
A fast adaptive multipole algorithm in three dimensions
Journal of Computational Physics
Boundary Element Programming in Mechanics
Boundary Element Programming in Mechanics
Applications of a fast multipole Galerkin in boundary element method in linear elastostatics
Computing and Visualization in Science
Fast multipole method based solution of electrostatic and magnetostatic field problems
Computing and Visualization in Science
Fast multipole method applied to elastostatic BEM-FEM coupling
Computers and Structures
A precorrected-FFT method for electrostatic analysis of complicated 3-D structures
IEEE Transactions on Computer-Aided Design of Integrated Circuits and Systems
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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.