eikonalfm 0.9.0

solving the (factored) eikonal equation with the Fast Marching method

Eikonal Fast Marching

eikonalfm is a Python (C++) extension which implements the Fast Marching method for the eikonal equation
| grad(tau)(x) |^2 = 1 / c^2(x),
and the factored eikonal equation
| (tau0 grad(tau1) + tau1 grad(tau0))(x) |^2 = 1 / c^2(x),
where tau0(x) = | x - x_s |.

References

• J. Sethian. Fast marching methods. SIAM Review, 41(2):199-235, 1999. doi: 10.1137/S0036144598347059. URL https://doi.org/10.1137/S0036144598347059
• Eran Treister and Eldad Haber. A fast marching algorithm for the factored eikonal equation. Journal of Computational Physics, 324:210-225, 2016.

Requirements

• Python 3
• numpy version 1.7 or above

Installation

Installation from PyPi:

pip install eikonalfm

Manual install from the repository:

git clone https://github.com/Daarknes/eikonalfm.git
cd eikonalfm
python setup.py

Examples

import numpy as np
import eikonalfm

c = np.ones((100, 100))
x_s = np.array([0, 0])
dx = np.array([1.0, 1.0])
order = 2

tau_fm = eikonalfm.fast_marching(c, x_s, dx, order)
tau_ffm = eikonalfm.factored_fast_marching(c, x_s, dx, order)

Note that the source position x_s describes an index-vector.