Grid Generation and Adaptation by Monge-Kantorovich Optimization in Two and Three Dimensions
Grid Generation and Adaptation by Monge-Kantorovich Optimization in Two and Three Dimensions
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二维和三维 Monge-Kantorovich 优化的网格生成和自适应
DOI：
10.1007/978-3-540-87921-3_33
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发表时间：
2008
期刊：
影响因子：
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通讯作者：
L. Chacón
中科院分区：
文献类型：
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作者：
J. Finn;G. Delzanno;L. Chacón
Monge-Ampère（MA）方程的推导，因为它是从涉及网格位移的变分原理得到的，在二维（2D）中概述。这个方程，蒙格-康托洛维奇（MK）优化的一个主要元素，讨论了在网格生成和网格适应的背景下。它表明，由MA方程生成的网格也满足交替变分原理最小化网格变形的方程。数值结果表明，网格缠结的鲁棒性。与现有的等分布变形法[G. Liao和D.安德森，应用分析44，285（1992）]进行了比较。一个配方给出更一般的物理域，包括那些弯曲的边界段。Monge-Ampère方程也是在三维（3D）中导出的。几个数值例子，更一般的2D域和3D，给出。
The derivation of the Monge-Ampère (MA) equation, as it results from a variational principle involving grid displacement, is outlined in two dimensions (2D). This equation, a major element of Monge-Kantorovich (MK) optimization, is discussed both in the context of grid generation and grid adaptation. It is shown that grids which are generated by the MA equation also satisfy equations of an alternate variational principle minimizing grid distortion. Numerical results are shown, indicating robustness to grid tangling. Comparison is made with the deformation method [G. Liao and D. Anderson,Appl. Analysis44, 285 (1992)], the existing method of equidistribution. A formulation is given for more general physical domains, including those with curved boundary segments. The Monge-Ampère equation is also derived in three dimensions (3D). Several numerical examples, both with more general 2D domains and in 3D, are given.
日本儿童和学生对 TIMSS 科学论文式任务的反应特征 (7) - 9 项任务分析结果的趋势 -
DOI：
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发表时间：
2005
期刊：
日本科学教育学会年会論文集 第29号
影响因子：
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作者：
中山 迅;大場裕子;猿田祐嗣
通讯作者：
猿田祐嗣