2021/01/20 by Gallouët, Anatole, Merigot, Quentin, Thibert, Boris · 1 citation
#Analysis of PDEs (math.AP) #Computational Geometry (cs.CG) #FOS: Computer and information sciences #FOS: Mathematics #Numerical Analysis (math.NA)
paper · doi:10.48550/arxiv.2101.08080
Generated Jacobian Equations have been introduced by Trudinger [Disc. cont. dyn. sys (2014), pp. 1663-1681] as a generalization of Monge-Ampère equations arising in optimal transport. In this paper, we introduce and study a damped Newton algorithm for solving these equations in the semi-discrete setting, meaning that one of the two measures involved in the problem is finitely supported and the other one is absolutely continuous. We also present a numerical application of this algorithm to the near-field parallel refractor problem arising in non-imaging problems.