About this code
This code creates the matrices in solving the Stokes equation over 3D domain.
See JSIAM2020_NS.pdf for an introduction of the problem.
This project does not provide the matrices needed for the a priori error estimation.
Xuefeng LIU, 2020/08/25 Updated: 2022/07/15
About the structure
There are four folders existing. In each folder, the setting file is prepared for a mesh with different size. But since the matrices will be huge, the matrix is not ready yet.
- Case_2020_08_25_Cube_N_4 (The matrix will be about 0.05G)
- Case_2020_08_25_Cube_N_8 (The matrix will be about 0.5G)
- Case_2020_08_25_Cube_N_16 (The matrix will be about 1.8G)
- Case_2020_08_25_Cube_N_32 (The matrix will be about 10G)
There is also a bin folder, which contains the commands to create matrix and solve the equation.
How to create matrix
- FEniCS package (http://www.fenicsproject.org)
- MATLAB or Octave (The create_matrix.sh use Octave as default. You can customize this as MATLAB.)
To create matrix for each folder, enter the bin folder and run create_matrix.sh:
cd ./bin/ chmod 755 * ./create_matrix.sh ../Case_2020_08_25_Cube_N_4/
Calculate the approximate solution
If the solution is needed to check the result, run get_solution.sh, which applies the Lagrange method to solve the equation.
cd ./bin/ ./get_solution.sh ../Case_2020_08_25_Cube_N_4/
About the directory
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