三维Monge-Ampere算子的离散化，介于宽 stencil 与 power diagram 之间
Discretization of the 3D Monge-Ampere operator, between Wide Stencils and Power Diagrams
AI总结：
本文提出一种单调（退化椭圆）离散化方法，用于三维Monge-Ampere算子，结合宽stencil方法与基于power diagram的最优传输离散化思想，提升精度并保证全局收敛性。
摘要：
我们介绍了一种单调（退化椭圆）的Monge-Ampere算子离散化方法，适用于在笛卡尔网格上离散的域。该方案在解的Hessian条件数一致有界时保持一致性。我们的方法继承了宽stencil方法的简洁性，但通过受power diagram基于的最优传输离散化思想的启发显著提高了精度。我们建立了用于离散方程组的阻尼牛顿求解器的全局收敛性。三维数值实验展示了该方案的效率。
英文摘要：
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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