A Damped Newton Algorithm for Generated Jacobian Equations
Computational Geometry
2021-01-21 v1 Numerical Analysis
Analysis of PDEs
Numerical Analysis
Abstract
Generated Jacobian Equations have been introduced by Trudinger [Disc. cont. dyn. sys (2014), pp. 1663-1681] as a generalization of Monge-Amp{\`e}re 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.
Cite
@article{arxiv.2101.08080,
title = {A Damped Newton Algorithm for Generated Jacobian Equations},
author = {Anatole Gallouët and Quentin Merigot and Boris Thibert},
journal= {arXiv preprint arXiv:2101.08080},
year = {2021}
}