Three-dimensional adaptive domain remeshing, implicit domain meshing, and applications to free and moving boundary problems

By Charles Dapogny, Cecile Dobrzynski, Pascal J. Frey. Journal of Computational Physics, 2014

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Shape optimization with a level set based mesh evolution method (2014, unknown): “The (vector) velocity ﬁeld V Ω is eventually derived once Ω has been associated a level set function φ , by using the usual extension of the normal vector ﬁeld n = ∇ φ |∇ φ | . f In practice we use the value of α given by 4 h 2 where h is the minimal size of elements (prescribed in the remeshing…”
Manufacturing Constraints and Multi-Phase Shape and Topology Optimization via a Level-Set Method (2014, methodology): “analytical optimum-topology solution of two beams at an angle of 45◦ that supports the applied load can be made. The two materials assumed have a ratio of 2:1 for the Young’s modulus and the same Poisson’s ratio (ν =0.3). The problem includes equality constraints on the volume of each of the materia”