JET MARCHING METHODS FOR SOLVING THE EIKONAL EQUATION

Samuel F. Potter

doi:10.1137/20M1366526

2021-12-20

Samuel F. Potter *

Maria Cameron

DOI：10.1137/20M1366526

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摘要

En 中文

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, thirdorder 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 providing the solvers, and from which the results of this paper can be reproduced easily.

Keyword:

eikonal equation

high-order solver

semi-Lagrangian solver

Hermite interpolation

direct solver

marching

期刊

SIAM Journal on Scientific Computing

IF:

2.6

论文数:

5.1K

被引数:

1.8W

机构

University System of Maryland

学者数:

6.5W

论文数: 5.6W

被引数: 113

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