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We introduce a monotone (degenerate elliptic) discretization of theMonge-Ampere operator, on domains discretized on cartesian grids. The scheme isconsistent provided the solution hessian condition number is uniformly bounded.Our approach enjoys the simplicity of the Wide Stencil method, butsignificantly improves its accuracy using ideas from discretizations of optimaltransport based on power diagrams. We establish the global convergence of adamped Newton solver for the discrete system of equations. Numericalexperiments, in three dimensions, illustrate the scheme efficiency.

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