A novel unconditionally stable explicit integration method for finite element method
| Autor: | Mianlun Zheng, Qianqian Tong, Zhiyong Yuan, Guian Zhang, Weixu Zhu |
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| Rok vydání: | 2017 |
| Předmět: |
Mathematical optimization
Spectral radius Explicit and implicit methods Equations of motion 020207 software engineering 02 engineering and technology 01 natural sciences Computer Graphics and Computer-Aided Design Transfer function Finite element method 010101 applied mathematics Matrix (mathematics) Nonlinear system Stability conditions 0202 electrical engineering electronic engineering information engineering Applied mathematics Computer Vision and Pattern Recognition 0101 mathematics Software Mathematics |
| Zdroj: | The Visual Computer. 34:721-733 |
| ISSN: | 1432-2315 0178-2789 |
| DOI: | 10.1007/s00371-017-1410-9 |
| Popis: | 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. |
| Databáze: | OpenAIRE |
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