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Discretization of the 3D Monge-Ampere operator, between Wide Stencils and Power Diagrams

Mirebeau, Jean-Marie (2015), Discretization of the 3D Monge-Ampere operator, between Wide Stencils and Power Diagrams, ESAIM: Mathematical Modelling and Numerical Analysis, 49, 5, p. 1511-1523. https://doi.org/10.1051/m2an/2015016

Type
Article accepté pour publication ou publié
External document link
https://hal.archives-ouvertes.fr/hal-01121508
Date
2015
Journal name
ESAIM: Mathematical Modelling and Numerical Analysis
Volume
49
Number
5
Pages
1511-1523
Publication identifier
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Author(s)
Mirebeau, Jean-Marie
Abstract (EN)
We introduce a monotone (degenerate elliptic) discretization of the Monge-Ampere operator, on domains discretized on cartesian grids. The scheme is consistent provided the solution hessian condition number is uniformly bounded. Our approach enjoys the simplicity of the Wide Stencil method, but significantly improves its accuracy using ideas from discretizations of optimal transport based on power diagrams. We establish the global convergence of a damped Newton solver for the discrete system of equations. Numerical experiments, in three dimensions, illustrate the scheme efficiency.
Subjects / Keywords
Viscosity solutions; monotone numerical scheme; finite difference methods; Monge−Ampere operator