Volume 44 Issue 1
Jan.  2023
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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

Algorithm Research Based on the PDE Sensitivity Filter

doi: 10.21656/1000-0887.430064
  • Received Date: 2022-03-01
  • Rev Recd Date: 2022-12-15
  • Available Online: 2023-01-06
  • Publish Date: 2023-01-15
  • 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.

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