Algorithm Research Based on the PDE Sensitivity Filter

MENG Huanli; ZHANG Qiliang; WANG Jie

doi:10.21656/1000-0887.430064

Volume 44 Issue 1

Jan. 2023

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Article Navigation > Applied Mathematics and Mechanics > 2023 > 44(1): 80-92

MENG Huanli, ZHANG Qiliang, WANG Jie. Algorithm Research Based on the PDE Sensitivity Filter[J]. Applied Mathematics and Mechanics, 2023, 44(1): 80-92. doi: 10.21656/1000-0887.430064

Citation:

MENG Huanli, ZHANG Qiliang, WANG Jie. Algorithm Research Based on the PDE Sensitivity Filter[J]. Applied Mathematics and Mechanics, 2023, 44(1): 80-92. doi: 10.21656/1000-0887.430064

Citation:

MENG Huanli, ZHANG Qiliang, WANG Jie. Algorithm Research Based on the PDE Sensitivity Filter[J]. Applied Mathematics and Mechanics, 2023, 44(1): 80-92. doi: 10.21656/1000-0887.430064

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Algorithm Research Based on the PDE Sensitivity Filter

doi: 10.21656/1000-0887.430064

1.
School of Systems Science and Engineering, SUN Yat-Sen University, Guangzhou 510006, P.R.China
2.
Tianjin Aerospace Long March Rocket Manufacturing Co. Ltd. , Tianjin 300462, P.R.China

Received Date: 2022-03-01
Rev Recd Date: 2022-12-15

Available Online: 2023-01-06

Publish Date: 2023-01-01

Abstract

Abstract

The PDE sensitivity filter can eliminate the checkerboard patterns and numerical instability existing in the topology optimization results of continuum structures, and the essence of the PDE sensitivity filter is the Helmholtz partial differential equation with Neumann boundary conditions. To solve the large-scale PDE sensitivity filter problem, the conjugate gradient algorithm, the multigrid algorithm and the multigrid preconditioned conjugate gradient algorithm were used to solve the algebraic equations obtained by finite element analysis, and the effects of accuracy, filter radius and grid numbers on the efficiency of topology optimization were studied. The results show that, compared with the conjugate gradient algorithm and the multi-grid algorithm, the multi-grid preconditioned conjugate gradient algorithm has the least number of iterations and the shortest running time, which greatly improves the efficiency of topology optimization.
- PDE filter,
- Helmholtz equation,
- multigrid algorithm,
- conjugate gradient algorithm,
- topology optimization

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References(20)

References

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