A fast accurate approximation method with multigrid solver for two-dimensional fractional sub-diffusion equation

This is a Reproduction Package as described in the manuscript "Three Empirical Principles for Computational Reproducibility and their Implementation: The Reproduction Package” by M. S. Krafczyk, A. Shi, A. Bhaskar, D. Marinov, & V. Stodden

"A fast accurate approximation method with multigrid solver for two-dimensional fractional sub-diffusion equation" implements an approximate solution method for the fractional sub-diffusion equation, as described in their paper. At each solution step, a large dimensional array has to be inverted to get the next step. For each inversion, a multigrid method is used to reduce the dimensionality of the matrix in question. Then an approximate inversion equation is applied when the dimensionality becomes small enough. After inversion, the solution is interpolated back to the full dimensionality.

Build Instructions

Requirements

Instructions were tested using Docker version 18.06.0-ce, build 0ffa825, on Ubuntu 16.04.5 LTS.

Building with Docker

docker build -t ${DOCKER_IMAGE_NAME} .

Run Instructions

Running with Docker

To start a container for the Docker image:

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

Run Everything

Within the Docker container, to run everything, building the code and running computational scripts for experiments, run

./run.sh

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

See sections below provide for details about the individual steps.

Building Code

Within the Docker container, run

./build.sh

After building, the resulting artifacts are binaries:

example1
example1_BDADI
example2
example2_BFSMGM
example3

Running Computational Scripts

Within the Docker container, run

./computation.sh

Output will be tables:

table1.csv
table2.csv
table3.csv
table4.csv

Expected tables are in directory expected_output/.

The script also runs check.sh, which checks the outputted tables against the expected ones under expected_output/, checking the final column, the error values.

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.

Acknowledgements

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.

Grant Acknowledgement

This work was partially funded by NSF grants OAC-1839010 and CNS-1646305.