DeepAI AI Chat
Log In Sign Up

Metasurfaces and Optimal transport

by   Cristian E. Gutiérrez, et al.

This paper provides a theoretical and numerical approach to show existence, uniqueness, and the numerical determination of metalenses refracting radiation with energy patterns. The theoretical part uses ideas from optimal transport and for the numerical solution we study and implement a damped Newton algorithm to solve the semi discrete problem. A detailed analysis is carried out to solve the near field one source refraction problem and extensions to the far field are also mentioned.


Optimal transport: discretization and algorithms

This chapter describes techniques for the numerical resolution of optima...

A Damped Newton Algorithm for Generated Jacobian Equations

Generated Jacobian Equations have been introduced by Trudinger [Disc. co...

A Newton algorithm for semi-discrete optimal transport with storage fees and quantitative convergence of cells

In this paper we will continue analysis of the semi-discrete optimal tra...

Computational Semi-Discrete Optimal Transport with General Storage Fees

We propose and analyze a modified damped Newton algorithm to solve the s...

Efficient preconditioners for solving dynamical optimal transport via interior point methods

In this paper we address the numerical solution of the quadratic optimal...

Stochastic Incremental Algorithms for Optimal Transport with SON Regularizer

We introduce a new regularizer for optimal transport (OT) which is tailo...

Physics Informed Convex Artificial Neural Networks (PICANNs) for Optimal Transport based Density Estimation

Optimal Mass Transport (OMT) is a well studied problem with a variety of...