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Metis.jl is a Julia wrapper to the Metis library which is a
library for partitioning unstructured graphs, partitioning meshes, and
computing fill-reducing orderings of sparse matrices.
Graph partitioning
Metis.partition calculates graph partitions. As an example, here we partition
a small graph into two, three and four parts, and visualize the result:
Metis.partition(g, 2)
Metis.partition(g, 3)
Metis.partition(g, 4)
Metis.partition calls METIS_PartGraphKway or METIS_PartGraphRecursive from the Metis
C API, depending on the optional keyword argument alg:
Metis.separator calculates a vertex separator
of a graph. Metis.separator calls METIS_ComputeVertexSeparator from the Metis C API.
As an example, here we calculate a vertex separator (green) of a small graph:
Metis.separator(g)
Fill reducing permutation
Metis.permutation calculates the fill reducing permutation
for a sparse matrices. Metis.permutation calls METIS_NodeND from the Metis
C API. As an example, we calculate the fill reducing permutation
for a sparse matrix S originating from a typical (small) FEM problem, and
visualize the sparsity pattern for the original matrix and the permuted matrix:
We can also visualize the sparsity pattern of the Cholesky factorization of
the same matrix. It is here clear that using the fill reducing permutation
results in a sparser factorization:
