solving the (factored) eikonal equation with the Fast Marching method
Project description
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.
Project details
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