Articles citing this article

The Citing articles tool gives a list of articles citing the current article.
The citing articles come from EDP Sciences database, as well as other publishers participating in CrossRef Cited-by Linking Program. You can set up your personal account to receive an email alert each time this article is cited by a new article (see the menu on the right-hand side of the abstract page).

Cited article:

Inverse freeform design in non-imaging optics: Hamilton’s theory of geometrical optics, optimal transport, and least-squares solvers

J. H. M. ten Thije Boonkkamp, K. Mitra, M. J. H. Anthonissen, L. Kusch, P. A. Braam and W. L. IJzerman
Frontiers in Physics 13 (2025)
https://doi.org/10.3389/fphy.2025.1518660

From Domain Decomposition to Model Reduction for Large Nonlinear Structures

Bertrand Leturcq and Patrick Le Tallec
Comptes Rendus. Mécanique 351 (S1) 573 (2024)
https://doi.org/10.5802/crmeca.168

A nonlinear least-squares convexity enforcing 𝐶⁰ interior penalty method for the Monge–Ampère equation on strictly convex smooth planar domains

Susanne Brenner, Li-yeng Sung, Zhiyu Tan and Hongchao Zhang
Communications of the American Mathematical Society 4 (14) 607 (2024)
https://doi.org/10.1090/cams/39

Hybridizable Discontinuous Galerkin Methods for the Two-Dimensional Monge–Ampère Equation

Ngoc Cuong Nguyen and Jaime Peraire
Journal of Scientific Computing 100 (2) (2024)
https://doi.org/10.1007/s10915-024-02604-3

Operator-Splitting/Finite Element Methods for the Minkowski Problem

Hao Liu, Shingyu Leung and Jianliang Qian
SIAM Journal on Scientific Computing 46 (5) A3230 (2024)
https://doi.org/10.1137/23M1590779

An adaptive least-squares algorithm for the elliptic Monge–Ampère equation

Alexandre Caboussat, Dimitrios Gourzoulidis and Marco Picasso
Comptes Rendus. Mécanique 351 (S1) 277 (2024)
https://doi.org/10.5802/crmeca.222

Mathematical model for inverse freeform design of a point-to-point two-reflector system

P. A. Braam, J. H. M. ten Thije Boonkkamp, M. J. H. Anthonissen, R. Beltman and W. L. IJzerman
Journal of the Optical Society of America A 41 (11) 2156 (2024)
https://doi.org/10.1364/JOSAA.532313

Solving the Dirichlet problem for the Monge–Ampère equation using neural networks

Kaj Nyström and Matias Vestberg
Journal of Computational Mathematics and Data Science 8 100080 (2023)
https://doi.org/10.1016/j.jcmds.2023.100080

A least-squares Galerkin approach to gradient and Hessian recovery for nondivergence-form elliptic equations

Omar Lakkis and Amireh Mousavi
IMA Journal of Numerical Analysis 42 (3) 2151 (2022)
https://doi.org/10.1093/imanum/drab034

A Least-Squares Method for the Solution of the Non-smooth Prescribed Jacobian Equation

Alexandre Caboussat, Roland Glowinski and Dimitrios Gourzoulidis
Journal of Scientific Computing 93 (1) (2022)
https://doi.org/10.1007/s10915-022-01968-8

A convexity enforcing $${C}^{{0}}$$ interior penalty method for the Monge–Ampère equation on convex polygonal domains

Susanne C. Brenner, Li-yeng Sung, Zhiyu Tan and Hongchao Zhang
Numerische Mathematik 148 (3) 497 (2021)
https://doi.org/10.1007/s00211-021-01210-x

Unified mathematical framework for a class of fundamental freeform optical systems

Martijn J. H. Anthonissen, Lotte B. Romijn, Jan H. M. ten Thije Boonkkamp and Wilbert L. IJzerman
Optics Express 29 (20) 31650 (2021)
https://doi.org/10.1364/OE.438920

A Finite Element/Operator-Splitting Method for the Numerical Solution of the Three Dimensional Monge–Ampère Equation

Hao Liu, Roland Glowinski, Shingyu Leung and Jianliang Qian
Journal of Scientific Computing 81 (3) 2271 (2019)
https://doi.org/10.1007/s10915-019-01080-4

A Newton Div-Curl Least-Squares Finite Element Method for the Elliptic Monge–Ampère Equation

Chad R. Westphal
Computational Methods in Applied Mathematics 19 (3) 631 (2019)
https://doi.org/10.1515/cmam-2018-0196

A Monge–Ampère Problem with Non-quadratic Cost Function to Compute Freeform Lens Surfaces

N. K. Yadav, J. H. M. ten Thije Boonkkamp and W. L. IJzerman
Journal of Scientific Computing 80 (1) 475 (2019)
https://doi.org/10.1007/s10915-019-00948-9

A Finite Element/Operator-Splitting Method for the Numerical Solution of the Two Dimensional Elliptic Monge–Ampère Equation

Roland Glowinski, Hao Liu, Shingyu Leung and Jianliang Qian
Journal of Scientific Computing 79 (1) 1 (2019)
https://doi.org/10.1007/s10915-018-0839-y

Numerical Approximation of Orthogonal Maps

Alexandre Caboussat, Roland Glowinski, Dimitrios Gourzoulidis and Marco Picasso
SIAM Journal on Scientific Computing 41 (6) B1341 (2019)
https://doi.org/10.1137/19M1243683

A Least-Squares/Relaxation Method for the Numerical Solution of the Three-Dimensional Elliptic Monge–Ampère Equation

Alexandre Caboussat, Roland Glowinski and Dimitrios Gourzoulidis
Journal of Scientific Computing 77 (1) 53 (2018)
https://doi.org/10.1007/s10915-018-0698-6

An Alternating Direction Method of Multipliers for the Numerical Solution of a Fully Nonlinear Partial Differential Equation Involving the Jacobian Determinant

Alexandre Caboussat and Roland Glowinski
SIAM Journal on Scientific Computing 40 (1) A52 (2018)
https://doi.org/10.1137/16M1094075

A least-squares method for the inverse reflector problem in arbitrary orthogonal coordinates

René Beltman, Jan ten Thije Boonkkamp and Wilbert IJzerman
Journal of Computational Physics 367 347 (2018)
https://doi.org/10.1016/j.jcp.2018.04.041

Splitting Methods in Communication, Imaging, Science, and Engineering

Roland Glowinski
Scientific Computation, Splitting Methods in Communication, Imaging, Science, and Engineering 251 (2016)
https://doi.org/10.1007/978-3-319-41589-5_8

Numerical Mathematics and Advanced Applications - ENUMATH 2013

Alexandre Caboussat and Roland Glowinski
Lecture Notes in Computational Science and Engineering, Numerical Mathematics and Advanced Applications - ENUMATH 2013 103 143 (2015)
https://doi.org/10.1007/978-3-319-10705-9_14

A Least-Squares Method for Optimal Transport Using the Monge--Ampère Equation

C. R. Prins, R. Beltman, J. H. M. ten Thije Boonkkamp, W. L. IJzerman and T. W. Tukker
SIAM Journal on Scientific Computing 37 (6) B937 (2015)
https://doi.org/10.1137/140986414

A New Augmented Lagrangian Approach for $L^1$-mean Curvature Image Denoising

M. Myllykoski, R. Glowinski, T. Kärkkäinen and T. Rossi
SIAM Journal on Imaging Sciences 8 (1) 95 (2015)
https://doi.org/10.1137/140962164

Modeling, Simulation and Optimization for Science and Technology

Alexandre Caboussat
Computational Methods in Applied Sciences, Modeling, Simulation and Optimization for Science and Technology 34 23 (2014)
https://doi.org/10.1007/978-94-017-9054-3_2