fvm-gmsfem

Implementation of the Generalized Multiscale Finite Element Method (GMsFEM) for solution problems in heterogeneous media with finite volume approximation on the fine grid.

My papers about GMsFEM:

• Chung ET, Efendiev Y, Li G, Vasilyeva M. Generalized multiscale finite element methods for problems in perforated heterogeneous domains PDF
• Akkutlu IY, Efendiev Y, Vasilyeva M. Multiscale model reduction for shale gas transport in fractured media PDF
• Vasilyeva M, Chung ET, Efendiev Y, Tyrylgin A. A three-level multi-continua upscaling method for flow problems in fractured porous media PDF

I would be grateful if you add citations to my relevant publications when you use it in your research.

Implementation of the method contains several parts:

• fine grid system generation (./systemT.py) - create mass and stiffness matrices and right - hand side vector
• local domains (coarse grid) generation (./local-domain/) - create files with coarse cells coordinates and cell indices in local domains
• multiscale basis function calculation (./gmsfem-basis/) - solve local spectral problems to generate and save multiscale basis functions
• projection matrix generation (./ms-rgen/) - load multiscale basis functions and create projection matrix R
• fine scale and multiscale solver (./solver/) - solve fine grid system or/and multiscale solver

Implementation based on the FEniCS (geometry objects, functions for saving and visualization) and PETSc (matrices, vectors and solvers).

How to use

Fine grid simulations:

1. run fenics container

docker run -ti -v $(pwd):/home/fenics/shared quay.io/fenicsproject/stable

2. create folders ./data/out/, ./data/modelF/
3. generate fine grid system for a given heterogeneous permeability field in ./data/perm/

python systemT.py

4. run fine grid solver in ./solver/

./solver F 50 1.0e-4 80 80 ../data/modelF/ ../data/out/ 1 ./ err.txt

Multiscale simulations:

1. create folders ./data/modelMs/omega10/, ./data/modelMs/eigen/, ./data/modelMs/dof/
2. local domains generations (coarse grid) in ./local-domain/

./omegas 2 ../data/omega10/ 10 0.1 0.0 10 0.1 0.0

3. multiscale basis generation in ./gmsfem-basis/

./run

4. generate R in ./ms-rgen/

./rgen 1 1600 121 ../data/modelMs/ 8

5. solve multiscale in ./solver/

./solver C 50 1.0e-4 80 80 ../data/modelF/ ../data/out/ 1936 ../data/modelMs/R100 err.txt