Native mesh ordering with Scotch 4.0

Sparse matrix reordering is a key issue for the the efficient factorization of sparse symmetric matrices, not only to reduce fill-in and operation count, but also to increase concurrency in the elimination tree, which is essential to achieve high speed-ups when solving the systems on parallel architectures. Most sparse matrix reordering software, when applied to finite-element or finite-volume meshes, require the construction of a nodal adjacency graph, the size of which is linear in the number of elements of the meshes, but quadratic in the number of nodes per element, resulting in a memory bottleneck for large 3D meshes of brick elements. This paper presents the native mesh ordering capabilities of the Scotch 4.0 software package, which has been designed so as to compute efficient orderings of mesh structures in a time which is still asymptotically quadratic function of number of nodes per element, but linear in space with respect to the number of elements and nodes, allowing for the processing of larger meshes on classical workstations.