Solving the Monge–Ampère equations for the inverse reflector problem

DOI10.1142/S0218202515500190zbMath1326.35365arXiv1404.7821MaRDI QIDQ5247096

Yasemin Hafizogullari, Andreas Platen, Kolja Brix

Publication date: 22 April 2015

Published in: Mathematical Models and Methods in Applied Sciences (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1404.7821

zbMATH Keywords

B-spline collocation methodelliptic Monge-Ampère equationinverse reflector problemcontraction mapping methods

Mathematics Subject Classification ID

Numerical computation using splines (65D07) Spectral, collocation and related methods for boundary value problems involving PDEs (65N35) PDEs in connection with optics and electromagnetic theory (35Q60) Numerical methods for inverse problems for boundary value problems involving PDEs (65N21) Nonlinear boundary value problems for nonlinear elliptic equations (35J66) Monge-Ampère equations (35J96)

Related Items

On the numerical solution of the far field refractor problem ⋮ Inverse reflector design for a point source and far-field target ⋮ Optimal transportation, modelling and numerical simulation ⋮ Monotone discretization of the Monge–Ampère equation of optimal transport ⋮ Trivariate spline collocation methods for numerical solution to 3D Monge-Ampère equation ⋮ A least-squares method for the inverse reflector problem in arbitrary orthogonal coordinates ⋮ An overview of mathematical modeling of geometric optics problems involving refraction ⋮ A Monge-Ampère problem with non-quadratic cost function to compute freeform lens surfaces ⋮ An Iterative Least-Squares Method for Generated Jacobian Equations in Freeform Optical Design

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