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Article Dans Une Revue ESAIM: Mathematical Modelling and Numerical Analysis Année : 2015

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

Résumé

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.
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hal-01121508 , version 1 (02-03-2015)

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Jean-Marie Mirebeau. Discretization of the 3D Monge-Ampere operator, between Wide Stencils and Power Diagrams. ESAIM: Mathematical Modelling and Numerical Analysis, 2015, 49 (5), pp.1511-1523. ⟨hal-01121508⟩
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