The objective of this work is to compare two topology optimization strategies, i.e. density-based (diffuse) and level-set-based (sharp), in thermal problems involving a heat conductor and an insulation material. The fundamental difference between the two methods lies in the representation of the materials’ interface: the density method allows for transitional regions whereas the level set one does not. Several regularization techniques, such as perimeter restriction, parameter ramping, level set gradient restriction and parametrization, are explored in order to enhance each method’s robustness and to decrease its sensitivity to initial conditions. It is shown that, in the two test problems investigated, the diffuse method was in general more robust than the sharp one. However, when combined with appropriate regularization techniques, the level set method lead to material distributions which were more optimal.

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