3 papers
math.OC2026
A Numerical Investigation of the RayleighFaberKrahn Inequality for Polyhedral Domains
Josué D. DÃaz-Avalos, Josué DÃaz-Avalos, Josué D. Díaz-Avalos +1
We present numerical results for the problem of minimizing the first Dirichlet eigenvalue of the Laplacian among three-dimensional convex polyhedra with a prescribed number of face…
math.OC2026
FormOpt: A FEniCSx toolbox for level set-based shape optimization supporting parallel computing
Josué D. DÃaz-Avalos, Antoine Laurain
This article presents the toolbox FormOpt for two- and three-dimensional shape optimization with parallel computing capabilities, built on the FEniCSx software framework. We introd…
math.OC2025
Optimization of centroidal Voronoi tessellations
Ernesto G. Birgin, Juan S. C. Franco, Antoine Laurain
In this paper, we investigate the optimization of Centroidal Voronoi Tessellations (CVT) under geometric constraints. For this purpose, we minimize a linear combination of the stan…