论文标题
搜索艾科纳尔方程的喷射行军方法
Jet Marching Methods for Solving the Eikonal Equation
论文作者
论文摘要
我们开发了一个紧凑的高阶半拉格朗日标签设定方法，用于解决艾科纳尔方程。这些求解器将共有1-二喷射的总1射流，并使用Hermite插值来近似于每个半拉格朗日更新本地的Eikonal和参数化特性。我们在任何维度上描述了非结构化网格的求解器，并在两个维度的常规网格上进行数值实验。我们的结果表明，这些求解器至少会产生二阶收敛，在特殊情况下，例如线性速度，eikonal及其梯度的收敛性三阶。我们还展示了如何使用基于细胞的插入剂来三个部分。计算出的第二个导数信息通常是二阶准确的，适用于局部求解传输方程。这提供了一种从Helmholtz方程的WKB近似中训练的预制器的方法。这些求解器专为在复杂的环境中计算helmholtz方程的高频近似而设计，据我们所知，这是具有这些属性的第一个求解器。我们提供了在线提供求解器的链接，并可以轻松地从中复制本文的结果。
We develop a family of compact high-order semi-Lagrangian label-setting methods for solving the eikonal equation. These solvers march the total 1-jet of the eikonal, and use Hermite interpolation to approximate the eikonal and parametrize characteristics locally for each semi-Lagrangian update. We describe solvers on unstructured meshes in any dimension, and conduct numerical experiments on regular grids in two dimensions. Our results show that these solvers yield at least second-order convergence, and, in special cases such as a linear speed of sound, third-order of convergence for both the eikonal and its gradient. We additionally show how to march the second partials of the eikonal using cell-based interpolants. Second derivative information computed this way is frequently second-order accurate, suitable for locally solving the transport equation. This provides a means of marching the prefactor coming from the WKB approximation of the Helmholtz equation. These solvers are designed specifically for computing a high-frequency approximation of the Helmholtz equation in a complicated environment with a slowly varying speed of sound, and, to the best of our knowledge, are the first solvers with these properties. We provide a link to a package online providing the solvers, and from which the results of this paper can be reproduced easily.
