BiotBrinkmanWithVorticityPaper

Repository that holds the Julia software and computational results reported in Section 5 of the paper "Robust finite element methods and solvers for the Biot-Brinkman equations in vorticity form" by R. Caraballo, C. W. In, A. F. Martín, and R. Ruiz-Baier. particular:

• The accuracy tests in Section 5.1 can be generated with the script available here for the 2D experiments, and with the script here for the 3D ones.
• The plots in Section 5.2 can be generated using the Pluto.jl interactive/reactive notebook available here. This notebook loads a set of BSON data files available here. This data files were in turn automatically generated using the DrWatson.jl script available here. These scripts are designed such that the user might seamlessly run new combination of physical and discretization parameter values. See below for instructions.
• The plots in Section 5.3 can be generated using the Pluto.jl interactive/reactive notebook available here. This notebook loads a set of BSON data files available here. This data files were in turn automatically generated using the DrWatson.jl script available here. These scripts are designed such that the user might seamlessly run new combination of physical and discretization parameter values. See below for instructions.

Instructions to generate and visualize Riesz mapping preconditioner evaluation results (Section 5.3)

IMPORTANT NOTE: The instructions below can be applied almost verbatim to generate the results in Section 5.2. The only difference being the scripts to be used, which are located in the BiotBrinkman3DConvergenceTests folder

IMPORTANT NOTE: As a pre-requisite to follow the instructions below, DrWatson.jl must be installed in the main julia environment, e.g., v1.9 if you have Julia 1.9. Please install it in the main julia environment before following the instructions in the sequel.

1. Select those combinations of parameter-values to be run by editing the dictionary created by the generate_param_dicts() function in the script available here.
2. Run the script:

   cd experiments/BiotBrinkmanVorticityPreconditionerTests/
   julia run_experiment.jl

   Note that the --project=XXX flag is not required in the call to the julia command. The script is smart enough in order to locate the Project.toml of the project in an ancestor directory. Upon completion, the results are generated in the data directory of the project, in particular in the data/BiotBrinkmanVorticityPreconditionerTests/commit-ID folder, where commit-ID denotes the latest commit in the repository. If you have changes in your local repository, then the BSON data files will be generated at data/BiotBrinkmanVorticityPreconditionerTests/commit-ID-dirty. The script is intelligent enough so that if it is interrupted and re-run, it will only run those combinations which are pending.
3. Visualize the results with the Pluto notebook as follows. Go to the root folder of the project and run the following command:

   julia --project=.
   

   Then, in the Julia REPL, run:

   import Pluto 
   Pluto.run(notebook="notebooks/BiotBrinkmanVorticityPreconditionerTests.jl") 

   this will trigger a web browser tab with the contents of the notebook. Finally, in the notebook, select the data directory with the results you would like to visualize using the "Select commit ID data directory" drop-down list.