标题： 水平集方法的特征线边界条件 显示英文标题

标题： Eikonal boundary condition for level set method

摘要： 本文中，我们提出在求解水平集公式中的对流或法向流方程时，在三维域内的多面体网格上采用eikonal方程作为边界条件。 由于水平集方法可以采用符号距离函数作为初始条件，因此在初始时刻，边界上的eikonal方程是一个合适的选择。 在以后的时刻强制施加eikonal方程于边界可以消除对传输方程通常需要的流入边界条件的需求。 在某些存在精确解的例子中，我们将所提出的方法与使用精确Dirichlet边界条件的方法进行了比较。 数值结果证实，与通常不可用的精确Dirichlet边界条件相比，使用eikonal边界条件在表面演化方面提供了相当的准确性和鲁棒性。 我们还展示了演化一般闭合曲面的数值结果。 显示英文摘要

摘要： In this paper, we propose to use the eikonal equation as a boundary condition when advective or normal flow equations in the level set formulation are solved numerically on polyhedral meshes in the three-dimensional domain. Since the level set method can use a signed distance function as an initial condition, the eikonal equation on the boundary is a suitable choice at the initial time. Enforcing the eikonal equation on the boundary for later times can eliminate the need for inflow boundary conditions, which are typically required for transport equations. In selected examples where exact solutions are available, we compare the proposed method with the method using the exact Dirichlet boundary condition. The numerical results confirm that the use of the eikonal boundary condition provides comparable accuracy and robustness in surface evolution compared to the use of the exact Dirichlet boundary condition, which is generally not available. We also present numerical results of evolving a general closed surface.