This repository contains a Matlab implementation of the data-driven mechanics for steady-state and transient mass diffusion problems formulated in terms of chemical potential field. A specific class of data-driven approach is adopted here, called distance-minimizing data-driven solvers. For more details on the subject the user of the code is directed to the papers in the literature.
- Poineer work in the data-driven mechanics https://doi.org/10.1016/j.cma.2016.02.001
- Extension to the dynamic problems https://doi.org/10.1002/nme.5716
- Variational framework of data-driven problems https://doi.org/10.1016/j.cma.2020.112898
This code provides:
- A very clean implementation of distance-minimizing data-driven solver.
- A procedural implementation of 2D finite element for scalar fields.
- Pre- and post-processing parsing functions for Gmsh and Paraview.
- This code can be easily extended to 3D by adding new Shape functions and Integration rules.
Author is fully aware that this code is a very naive approach towards a very complex subject (finite-elements). There exist much better and robust implementations and open source packages e.g., deal.II and FEniCS Project. However, reporting of any comment, found bugs, improvements and dicussions on the theoratical and implementation aspects are highly appreciated. You can contact me at engineerabdullah@ymail.com .
This code is purely for educational purposes. All rights are preseved, however, author shall not be liable in any event caused by the use of the code.
Please don't forget to cite this work as
Waseem, A. (2020) A Matlab implementation of data-driven diffusion mechanics for steady-state and transient diffusion problems. Retrieved from https://github.com/AbdullahWaseem/Data-Driven-Diffusion-Mechanics