Fedorenko - Repository of Multigrid Solvers
A collection of multigrid solvers in both cell-centered and vertex-centered configurations.
There are 1D, 2D and 3D versions for both cases, all packed into a single repository to ease the development of multigrid solvers for those who wish to write one.
All the solvers are written in Python.
They are derived from the repositories MG-Lite, which demonstrates a 1D multigrid solver with GUI, and Orion, a finite-difference fluid flow solver written in Python.
The cell-centered versions have the prefix "cc", and the vertex-centered versions have the prefix "vc". GPU parallel versions of the solvers (under development) have the prefix "gpu", and are based on the cell-centered configuration. The suffix indicates the dimensionality of the solver. All of them solve the Poisson equation on a domain with Dirichlet boundary conditions. They print the convergence of the residual with V-cycles, and plot it at the end of the run.
The earliest version of multigrid algorithm is attributed to a paper by R. P. Fedorenko. Hence the name of this repository.
Please make sure that the following Python modules are installed before running any of the codes.
numpy- All array manipulations are performed using NumPydatetime- The execution time is measured using this modulematplotlib- Results are plotted using thematplotliblibrary
License
Fedorenko is an open-source package made available under the New BSD License.
References
Below is a list of useful articles that explains the multigrid-method used here.
Articles on multi-grid methods
- http://math.mit.edu/classes/18.086/2006/am63.pdf
- http://www.mgnet.org/mgnet-tuts.html
- R. P. Fedorenko, “The speed of convergence of one iterative process”, Zh. Vychisl. Mat. Mat. Fiz., 4:3 (1964), 559–564; U.S.S.R. Comput. Math. Math. Phys., 4:3 (1964), 227–235