Sequential topology optimization: SIMP initialization for level-set boundary refinement

Density-based topology optimization methods such as SIMP enable efficient topological exploration but produce diffuse material boundaries that require interpretation before manufacturing. Level-set methods maintain sharp interfaces but are sensitive to the initial design. This paper presents a sequential framework that addresses these complementary limitations through a signed distance function (SDF)-based geometry transfer, formulated for three-dimensional meshes. The SIMP density distribution is converted into an SDF that initializes subsequent level-set boundary refinement. From the level-set perspective, the SIMP-derived initialization mitigates sensitivity to the initial design. From the SIMP perspective, the level-set stage acts as optimization-driven post-processing that produces manufacturing-ready boundaries. Validation on three-dimensional cantilever and MBB benchmarks demonstrates compliance comparable to standalone level-set optimization, with up to 4.6x wall-clock speedup on the cantilever case. The full implementation is released under an open-source license to support reproducibility.