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gmsfem-fem-fvm

Implementation of the Generalized Multiscale Finite Element Method (GMsFEM) for solution problems in heterogeneous or/and perforated media based on the system representation (fvm or fem fine grid approximation)

My papers about multiscale method:

  • Chung ET, Efendiev Y, Li G, Vasilyeva M. Generalized multiscale finite element methods for problems in perforated heterogeneous domains 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:

  • fine grid system generation (./systemFEM.py and ./systemFVM.py) - create mass and stiffness matrices and right - hand side vector (create fine grid system)
  • 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 (use system generated from first step)
  • 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 (use system generated from first step)

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

  1. create folders ./data/out/, ./data/modelF/

  2. generate fine grid system

python systemFEM.py

or

python systemFVM.py

  1. run fine grid solver in ./solver/

./solver F 0 20 0.0003 80 6400 ../data/modelF/ ../data/out/ 1 ./ err.txt

or

./solver F 1 20 0.003 ../data/mesh/mesh-p 6101 ../data/modelF/ ../data/out/ 1 ./ err.txt

or

./solver F 1 20 0.03 ../data/mesh/mesh-h 6373 ../data/modelF/ ../data/out/ 1 ./ err.txt

Multiscale simulations:

  1. create folders ./data/modelMs/omega10fem/, ./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

or

./omegas 2 ../data/modelMs/omega10/ 10 0.2 -1.0 10 0.2 -1.0

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

./run

  1. generate R in ./ms-rgen/

./rgen 1 6400 121 ../data/modelMs/ 16

or

./rgen 1 6101 121 ../data/modelMs/ 16

or

./rgen 1 6373 121 ../data/modelMs/ 16

  1. solve multiscale in ./solver/

./solver C 0 20 0.0003 80 6400 ../data/modelF/ ../data/out/ 1936 ../data/modelMs/R100 err.txt

or

./solver C 1 20 0.003 ../data/mesh/mesh-p 6101 ../data/modelF/ ../data/out/ 1936 ../data/modelMs/R100 err.txt

or

./solver C 1 20 0.03 ../data/mesh/mesh-h 6373 ../data/modelF/ ../data/out/ 1936 ../data/modelMs/R100 err.txt