Discretization of the 3D Monge-Ampere operator, between Wide Stencils and Power Diagrams
Discretization of the 3D Monge-Ampere operator, between Wide Stencils and Power Diagrams
复制标题
宽模板和功率图之间 3D Monge-Ampere 算子的离散化
DOI：
10.1051/m2an/2015016
复制
发表时间：
2015
期刊：
影响因子：
--
通讯作者：
J. Mirebeau
中科院分区：
文献类型：
--
作者：
J. Mirebeau
我们在笛卡尔网格上离散的区域上引入了Monge-Ampere算子的单调(退化椭圆)离散化。如果解的Hessian条件数一致有界，则该方案是一致的。我们的方法享受了宽模板方法的简单性，但使用了基于功率图的最优运输离散化的思想，显著提高了其精度。我们建立了离散方程组的阻尼牛顿求解器的全局收敛性质。三维数值实验表明了该格式的有效性。
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.