An adaptive mesh redistribution method for nonlinear Hamilton--Jacobi equations in two-and three-dimensions
An adaptive mesh redistribution method for nonlinear Hamilton--Jacobi equations in two-and three-dimensions
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DOI：
10.1016/s0021-9991(03)00192-x
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发表时间：
2003-07
影响因子：
4.1
通讯作者：
Huazhong Tang;T. Tang;Pingwen Zhang
中科院分区：
文献类型：
--
作者：
Huazhong Tang;T. Tang;Pingwen Zhang
提出了一种求解二维和三维非线性Hamilton-Jacobi方程和水平集方程的自适应网格重分布方法。我们的方法包括两个关键成分：在更新的自适应网格上的非保守二阶插值，以及一类适用于Hamilton-Jacobi问题的监视函数（或指示器）。提出的自适应网格方法将逻辑域中的均匀网格转换为物理域中解或其导数为奇异或近奇异的网格点。此外，所提出的AMR方法保持了二阶收敛速度。大量的数值实验证明了所提出的自适应网格算法的有效性和鲁棒性。
This paper presents an adaptive mesh redistribution (AMR) method for solving the nonlinear Hamilton–Jacobi equations and level-set equations in two- and three-dimensions. Our approach includes two key ingredients: a non-conservative second-order interpolation on the updated adaptive grids, and a class of monitor functions (or indicators) suitable for the Hamilton–Jacobi problems. The proposed adaptive mesh methods transform a uniform mesh in the logical domain to cluster grid points at the regions of the physical domain where the solution or its derivative is singular or nearly singular. Moreover, the formal second-order rate of convergence is preserved for the proposed AMR methods. Extensive numerical experiments are performed to demonstrate the efficiency and robustness of the proposed adaptive mesh algorithm.