Filters in topology optimization based on diffusion tensor of partial differential equations

In order to eliminate numerical instabilities efficiently in topology optimization, an initial-boundary value model of diffusion tensor of partial differential equations was established. Together with Neumann conditions to expand boundary, finite difference method was used to solve the model. The model integrated smoothly into topology optimization circle, and was aimed at element density and objective function sensitivity for filtering operations respectively. At last, the examples checked the effectiveness and flexibility of the two methods. Results illustrate that objective function sensitivity filtering can keep boundary clarity, but needs more filtering iteration number. However element density filtering owns high computational filtering efficiency, but has vague boundary.