Discontinuous Galerking Reduced basis finite element heterogeneous multiscale method

A short Matlab implementation of 2D and 3D multiscale Stokes to Darcy problems using discontinuous Galerkin methods at the macro scale and reduced basis methods for the FE discretization of Stokes micro problems. Here you can find Matlab codes that reproduce the numerical experiments presented in this paper.

Download

  • code - the minimal code that can reproduce the experiments from the article
  • data - all the data that the code produces. Some parts of the experiments (computing reference permeability or reference solution) are demanding or time-consuming. By downloading this data and unzipping them into experiments/computed/ you can jump to any experiment you like without precomputation.
  • AGMG - to run some of the 3D experiments we used this algebraic multigrid solver. The software is free for academic use but you need to contact the author to download it. The installation simple, the AGMG Matlab files need to be just included in the Matlab path.

Instructions

To start you need a recent version of Matlab (2010 or later should work). Download and unzip the code and run the script setpath.m. This will add to path the whole program and also the scripts that are needed to run the experiments. These scripts are located in experiments/. Inside this folder there is another README file that will help you run the experiments.

References

If you use this code in your research please cite the following paper:

@unpublished{AbdulleBudacDG16,
    author = {Abdulle, Assyr and Bud{\'a}{\v{c}}, Ondrej},
    title = {A discontinuous {G}alerkin reduced basis numerical homogenization method for fluid flow in porous media},
    year = {2016},
    documenturl = {https://infoscience.epfl.ch/record/213835/files/abd_budac_Gakuto_FE-HMM_abd.pdf},
    note = {submitted to SIAM J. Sci. Comput.}
}

If this code was helful, let us know, we will be happy to hear about how you used it. Moreover, any comments and bug reports are welcome.

Contact

ANMC web page  |  Assyr Abdulle  |  Ondrej Budac