Monotone and consistent discretization of the Monge-Ampère operator
Monotone and consistent discretization of the Monge-Ampère operator
复制标题
Monge-Ampère 算子的单调且一致的离散化
DOI：
10.1090/mcom/3080
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发表时间：
2014
期刊：
影响因子：
--
通讯作者：
J. Mirebeau
中科院分区：
文献类型：
--
作者：
J. Benamou;F. Collino;J. Mirebeau
我们引入了一种新的蒙日-安培算子的离散化方法，它同时是一致的和退化的椭圆，因此在应用中是精确的和鲁棒的。这些性质是通过利用离散域的算术结构来实现的，假设是一个二维笛卡尔网格。我们的方案结构简单，但其分析依赖于在数值分析中很少遇到的原始工具，例如二维晶格的几何形状，以及称为Stern-Brocot树的算术结构。数值实验证明了该方法的有效性。
We introduce a novel discretization of the Monge-Ampere operator, simultaneously consistent and degenerate elliptic, hence accurate and robust in applications. These properties are achieved by exploiting the arithmetic structure of the discrete domain, assumed to be a two dimensional cartesian grid. The construction of our scheme is simple, but its analysis relies on original tools seldom encountered in numerical analysis, such as the geometry of two dimensional lattices, and an arithmetic structure called the Stern-Brocot tree. Numerical experiments illustrate the method's efficiency.