Spatial gradient interface detection in topology optimization for an unstructured mesh

Spatial gradient calculations are regularly applied in topology optimization and typically used for detecting material distribution boundaries, interfaces, and overhanging features. While adopted for a variety of applications, the current approaches in literature are restricted to perfectly uniform mapped-meshing strategies or require element shape function vectors to complete computations, both of which are potential limitations when solving practical problems with commercial finite element solvers. To address these drawbacks, this brief note presents a technique for calculating spatial gradients using a neighbouring element search strategy, using the gradient norm, thinning, and thresholding calculations to determine a nearly discrete interface indicator. The proposed technique is generalized for a 3D unstructured mesh and applicable when using black-box finite element solvers. The technique is validated on three sample problems with increasing geometric and mesh discretization complexity to demonstrate and suggest its effectiveness for topology optimization in 2D and 3D.