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首页> 外文期刊>Journal of Computational Physics >HIGH ORDER TWO DIMENSIONAL NONOSCILLATORY METHODS FOR SOLVING HAMILTON-JACOBI SCALAR EQUATIONS
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HIGH ORDER TWO DIMENSIONAL NONOSCILLATORY METHODS FOR SOLVING HAMILTON-JACOBI SCALAR EQUATIONS

机译：求解Hamilton-Jacobi标量方程的高阶二维非振动方法

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摘要

For the computation of nonlinear solutions of Hamilton-Jacobi scalar equations in two space dimensions, we develop high order accurate numerical schemes that can be applied to complicated geometries. Previously, the recently developed essentially nonoscillatory (ENO) technology has been applied in simple domains like squares or rectangles using dimension-by-dimension algorithms. On arbitrary two dimensional closed or multiply connected domains, first order monotone methods were used. In this paper, we propose two different techniques to construct high order accurate methods using the ENO philosophy. Namely, any arbitrary domain is triangulated by finite elements into which two dimensional ENO polynomials are constructed. These polynomials are then differentiated to compute a high order accurate numerical solution. These new techniques are shown to be very useful in the computation of numerical solutions of various applications without significantly increasing CPU running times as compared to dimension-by-dimension algorithms. Furthermore, these methods are stable and no spurious oscillations are detected near singular points or curves. (C) 1996 Academic Press, Inc. [References: 17]
机译：为了在两个空间维度上计算Hamilton-Jacobi标量方程的非线性解，我们开发了可应用于复杂几何形状的高阶精确数值方案。以前，最近开发的本质上非振荡（ENO）技术已使用逐维算法应用于正方形或矩形等简单领域。在任意二维封闭或多重连接域上，使用一阶单调方法。在本文中，我们提出了两种使用ENO原理构造高阶精确方法的不同技术。即，任意域都由构成二维ENO多项式的有限元三角剖分。然后对这些多项式进行微分，以计算出高阶准确的数值解。与逐维算法相比，这些新技术在计算各种应用程序的数值解时非常有用，而不会显着增加CPU运行时间。而且，这些方法是稳定的，并且在奇异点或曲线附近未检测到任何寄生振荡。 （C）1996 Academic Press，Inc. [参考：17]

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