The Visual Computer

, Volume 34, Issue 5, pp 721–733 | Cite as

A novel unconditionally stable explicit integration method for finite element method

  • Mianlun Zheng
  • Zhiyong Yuan
  • Qianqian Tong
  • Guian Zhang
  • Weixu Zhu
Original Article


Physics-based deformation simulation demands much time in integration process for solving motion equations. To ameliorate, in this paper we resort to structural mechanics and mathematical analysis to develop a novel unconditionally stable explicit integration method for both linear and nonlinear FEM. First we advocate an explicit integration formula with three adjustable parameters. Then we analyze the spectral radius of both linear and nonlinear dynamic transfer function’s amplification matrix to obtain limitations for these three parameters to meet unconditional stability conditions. Finally, we theoretically analyze the accuracy property of the proposed method so as to optimize the computational errors. The experimental results indicate that our method is unconditionally stable for both linear and nonlinear systems and its accuracy property is superior to both common and recent explicit and implicit methods. In addition, the proposed method can efficiently solve the problem of huge computation cost in integration procedure for FEM.


Finite element method Implicit integration Explicit integration Unconditionally stable 



This work is supported by the Science and Technology Program of Wuhan, China, under Grant No. 2016010101010022; National Natural Science Foundation of China under Grant No. 61373107.

Supplementary material (26.2 mb)
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© Springer-Verlag Berlin Heidelberg 2017

Authors and Affiliations

  1. 1.School of ComputerWuhan UniversityWuhanChina

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