Reordering edges and elements in unstructured meshes to reduce execution time in Finite Element Computations


re-enumeración de lados y elementos
formulación de elementos finitos
reducción de ancho de banda y tiempo de ejecución
matriz esparcida por vector RCM reordering
finite element
bandwidth reduction of stiffness matrices
edge and element graphs of the mesh

How to Cite

Ortigoza Capetillo, G. M., Lorandi Medina, A. P., & García Reynoso, A. C. (2018). Reordering edges and elements in unstructured meshes to reduce execution time in Finite Element Computations. Nova Scientia, 10(20), 263–279.


Reverse Cuthill McKee (RCM) reordering can be applied to either edges or elements of unstructured meshes (triangular/tetrahedral) , in accordance to the respective finite element formulation,  to reduce the bandwidth of stiffness matrices . Grid generators are mainly designed for nodal based finite elements. Their output is a list of nodes (2d or 3d) and an array describing element connectivity, be it triangles or tetrahedra. However,  for edge-defined finite element formulations a numbering of the edges is required. Observations are reported for Triangle/Tetgen Delaunay grid generators and for the sparse structure of the assembled matrices in both edge- and element-defined formulations. The RCM is a renumbering algorithm traditionally applied to the nodal graph of the mesh. Thus, in order to apply this renumbering to either the edges or the elements of the respective finite element formulation,  graphs of the mesh were generated. Significant bandwidth reduction was obtained. This translates to reduction in the execution effort of the sparse-matrix-times-vector product. Compressed Sparse Row format was adopted and the matrix-times-vector product was implemented in an OpenMp parallel routine.


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