Journal
ESAIM-MATHEMATICAL MODELLING AND NUMERICAL ANALYSIS-MODELISATION MATHEMATIQUE ET ANALYSE NUMERIQUE
Volume 49, Issue 5, Pages 1511-1523Publisher
EDP SCIENCES S A
DOI: 10.1051/m2an/2015016
Keywords
Viscosity solutions; monotone numerical scheme; finite difference methods; Monge-Ampere operator
Categories
Ask authors/readers for more resources
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 [B.D. Froese and A.M. Oberman, J. Comput. Phys. 230 (2011) 818-834.], but significantly improves its accuracy using ideas from discretizations of optimal transport based on power diagrams [F. Aurenhammer, F. Hoffmann and B. Aronov, Algorithmica (1998)]. 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.
Authors
I am an author on this paper
Click your name to claim this paper and add it to your profile.
Reviews
Recommended
No Data Available