I am working on topology optimization using the parametric level set method. Regardless of the methodology, I thought it might be a generic problem in Topology optimization with which many researchers in the field have faced. The problem is that I cannot achieve smooth boundaries even though I am using the level-set method to produce smooth boundaries. I am using two different grids and meshes for the mechanical and the level-set domains. I thought I needed to increase the number of Finite elements from 350 to 1000, but nothing changed, you can see it from the bottom right figure. Nor did increasing the number of grid cells in the level set domain improve my result.
Thank you in advance for your help.
Best regards,
Farzad
Dear Farzad, topology optimisation does not necessarily lead to a smooth solution. Are you sure the optimal solution for your problem is smooth? If not, it might well happen that the numerical optimum becomes less and less smooth as the grid is refined.
Dear Roberto,
Thank you for your reply. Since I use a standard geometry, and strain energy density is my objective function, I expect a smooth geometry. Thank you anyway for your time and consideration.
You can consider adding a regularization term, such as the total variation of the level set function, to your optimization model.
Dear Richard,
Thank you for your comment. I have actually tried different regularization methods. I have also made the objective function dimensionless in order to be sure of everything. However, none of the above strategies has led to a reliable solution. Thank you anyway for taking the time.
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