Monotone discretization of the Monge–Ampère equation of optimal transport

DOI10.1051/m2an/2022029zbMath1496.65197OpenAlexW3188069195MaRDI QIDQ5074257

Guillaume Bonnet, Jean-Marie Mirebeau

Publication date: 9 May 2022

Published in: ESAIM: Mathematical Modelling and Numerical Analysis (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1051/m2an/2022029

zbMATH Keywords

convergence analysisMonge-Ampère equationoptimal transportmonotone finite difference schemes

Mathematics Subject Classification ID

Stability and convergence of numerical methods for boundary value problems involving PDEs (65N12) Degenerate elliptic equations (35J70) Finite difference methods for boundary value problems involving PDEs (65N06) Monge-Ampère equations (35J96)

Related Items (2)

The second boundary value problem for a discrete Monge-Ampère equation ⋮ A Convergent Quadrature-Based Method for the Monge–Ampère Equation

Cites Work

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• Far-field reflector problem and intersection of paraboloids
• Numerical solution of the optimal transportation problem using the Monge-Ampère equation
• The near field refractor
• Weak solutions of one inverse problem in geometric optics
• An entropic optimal transport numerical approach to the reflector problem
• \(C^{1}\) regularity of solutions of the Monge-Ampère equation for optimal transport in dimension two
• The refractor problem in reshaping light beams
• Viscosity solutions of fully nonlinear second-order elliptic partial differential equations
• Two remarks on Monge-Ampère equations
• Monotone mixed finite difference scheme for Monge-Ampère equation
• A computational fluid mechanics solution to the Monge-Kantorovich mass transfer problem
• Single pass computation of first seismic wave travel time in three dimensional heterogeneous media with general anisotropy
• A convergent finite difference method for computing minimal Lagrangian graphs
• A convergent finite difference method for optimal transport on the sphere
• Convergence of a Newton algorithm for semi-discrete optimal transport
• On the numerical solution of the far field refractor problem
• Regularity of potential functions of the optimal transportation problem
• Efficient fast marching with Finsler metrics
• The Monge–Ampère equation and its link to optimal transportation
• The convex envelope is the solution of a nonlinear obstacle problem
• Discretization of the 3d monge−ampere operator, between wide stencils and power diagrams
• Low-dimensional lattices. III. Perfect forms
• Polar factorization and monotone rearrangement of vector‐valued functions
• User’s guide to viscosity solutions of second order partial differential equations
• Determination of reflector surfaces from near-field scattering data
• Convergence Framework for the Second Boundary Value Problem for the Monge--Ampère Equation
• Convergent Filtered Schemes for the Monge--Ampère Partial Differential Equation
• Monotone and Second Order Consistent Scheme for the Two Dimensional Pucci Equation
• Finite element approximation of the Isaacs equation
• Minimal convex extensions and finite difference discretisation of the quadratic Monge–Kantorovich problem
• Riemannian Fast-Marching on Cartesian Grids, Using Voronoi's First Reduction of Quadratic Forms
• Solving the Monge–Ampère equations for the inverse reflector problem
• A fast algorithm for the two dimensional HJB equation of stochastic control
• Convergent Semi-Lagrangian Methods for the Monge--Ampère Equation on Unstructured Grids
• Monotone and consistent discretization of the Monge-Ampère operator
• The Monge-Ampère equation
• Optimal Transport

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