A simple two dimensional geometric multigrid solver for poisson equation.
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MGPCG.py
README.md
example3d.py
example_FMG.py
example_FMG_defcor.py
example_MGVCG.py
example_Vcycle.py
example_defcor.py
mgd2d.py
mgd3d.py
mgd3d_vec.py

README.md

GeometricMultigrid

A simple 2D and 3D geometric multigrid solver for poisson equation in python. It uses numpy.

             _______ _______ _______ _______ 
            |       :       |       :       |
            |   +   :   +   |   +   :   +   |
            |.......@.......|.......@.......|
            |       :       |       :       |
            |   +   :   +   |   +   :   +   |
            |_______:_______#_______:_______|
            |       :       |       :       |
            |   +   :   +   |   +   :   +   |
            |.......@.......|.......@.......|
            |       :       |       :       |
            |   +   :   +   |   +   :   +   |
            |_______:_______|_______:_______|

Details:

  • Smoother: Two color Gauss-Seidel
  • Restriction: Nearest points average
  • Prolongation: Multi-linear interpolation
  • V cycle and FMG

The examples show V cycle and FMG in action. An example script demonstrates the method of deferred correction to obtain 4th order accuracy.