h_j \neq \emptyset$. This can be done, for instance, by triangulating $\Omega$ and choosing for each vertex $i$ in the triangulation a function $h_i$ with support contained in all triangles adjacent to the vertex $i$.

We can now directly create a visual representation for the various hypergraph representations of the matrix $A$ ():

1.  for the symmetric, bipartite, column-net, and row-net representations, we map each vertex $i$, $r_i$, and $c_i$ to the center of $\supp h_i$ in ${\mathbf{R}}^d$,

2.  for the finegrain representation, we map each vertex $v_{i \, j}$ to the center of $\supp h_i \cap \supp h_j$ in ${\mathbf{R}}^d$.

Thus, in this case, we can generate a visual representation from our original problem with little extra effort.

However, not all matrices have an immediate geometric origin (e.g. `twotone`), so we would like to be able to create such a visual representation ourselves if it cannot be provided directly. Hence, we will continue by discussing how to create such a visual representation in . In , we show how to use visual representations for hypergraph partitioning, and in we apply this in the context of sparse LU decomposition. We conclude by implementing these methods and comparing them with both 