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A Fast Marching Algorithm for the Factored Eikonal Equation

"A fast marching algorithm for the factored eikonal equation" discusses an algorithm for solving the factored eikonal equation. Practically, this can be used to perform a kind of slowness tomography whereby travel times from some source within a material can be used to determine the slowness of an object with respect to position throughout the object.

Build Instructions

To run the software in this package, all you need is an appropriate Docker installation.


Instructions were tested using

  • Docker version 18.06.0-ce, build 0ffa825, on Ubuntu 16.04.5 LTS.
  • Docker version 19.03.1, build 74b1e89, on Mac OS Mojave (10.14.6)

Building with Docker

The Dockerfile handles installation of all necessary dependencies. Simply execute the following:

docker build -t ${DOCKER_IMAGE_NAME} .

Run Instructions

Running the Docker container

To start a container for the Docker image:

docker run -it --rm -v $(pwd):/Scratch ${DOCKER_IMAGE_NAME}

Initialize the Julia environment

Before running the experiments, you must first run

./ init

This downloads necessary Julia packages.

Run the experiments

In order to run the experiments, you use

./ run <num 2d refinements> <num 3d refinements>

Output will be written to results/results_<x>_<y>.txt where x is num 2d refinements and y is num 3d refinements.

This command also creates the figures for the experiment. They can be found in figures/.

Check the experiment results

In order to check the results of the experiment, you use

./ check <num 2d refinements> <num 3d refinements>

The expected output to be compared against is found in expected_output/.

The expected figures are found in expected_figures/, however the script does not compare these with the generated figures.

This command will let you know if the results match what is expected or not.

The script that checks equality to within a reasonable degree is examples/ If you wish to tighten or loosen the margin of error, modify that file.

Run Everything

To initilize, run the experiments, and check the results with one command, use

./ all <num 2d refinements> <num 3d refinements>

Please be aware of computational efforts for the scripts. More details can be found here.

Notes about Running All Rows

To reproduce all 6 rows from the article, use 6 as both num 2d refinements and num 3d refinements. Note that it does consume a lot of memory.

Reproduction Notes

We kept track of our progress and issues inside notes.txt. We also have an jupyter notebook showing this progress over time ReproducibilityPlot.ipynb.


We want acknowledge the authors for their fine work on this experiment. We succeeded with this project where many others had failed. The authors should be commended on putting together high quality work.

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