TY - JOUR
T1 - Node and element resequencing using the Laplacian of a finite element graph
T2 - Part II—Implementation and numerical results
AU - Paulino, Glaucio H.
AU - Menezes, Ivan F.M.
AU - Gattass, Marcelo
AU - Mukherjee, Subrata
PY - 1994/5/15
Y1 - 1994/5/15
N2 - In Part I of this work, Paulino et al.1 have presented an algorithm for profile and wavefront reduction of large sparse matrices of symmetric configuration. This algorithm is based on spectral properties of a Finite Element Graph (FEG), An FEG has been defined as a nodal graph G, a dual graph G* or a communication graph G˙ associated with a generic finite element mesh. The novel algorithm has been called Spectral FEG Resequencing (SFR). This algorithm has specific features that distinguish it from previous algorithms. These features include (1) use of global information in the graph, (2) no need of a pseudoperipheral vertex or the endpoints of a pseudodiameter, and (3) no need of any type of level structure of the FEG. To validate this algorithm in a numerical sense, extensive computational testing on a variety of problems is presented here. This includes algorithmic performance evaluation using a library of benchmark test problems which contains both connected and non‐connected graphs, study of the algebraic connectivity (λ2) of an FEG, eigensolver convergence verification, running time performance evaluation and assessment of the algorithm on a set of practical finite element examples. It is shown that the SFR algorithm is effective in reordering nodes and/or elements of generic finite element meshes. Moreover, it computes orderings which compare favourably with the ones obtained by some previous algorithms that have been published in the technical literature.
AB - In Part I of this work, Paulino et al.1 have presented an algorithm for profile and wavefront reduction of large sparse matrices of symmetric configuration. This algorithm is based on spectral properties of a Finite Element Graph (FEG), An FEG has been defined as a nodal graph G, a dual graph G* or a communication graph G˙ associated with a generic finite element mesh. The novel algorithm has been called Spectral FEG Resequencing (SFR). This algorithm has specific features that distinguish it from previous algorithms. These features include (1) use of global information in the graph, (2) no need of a pseudoperipheral vertex or the endpoints of a pseudodiameter, and (3) no need of any type of level structure of the FEG. To validate this algorithm in a numerical sense, extensive computational testing on a variety of problems is presented here. This includes algorithmic performance evaluation using a library of benchmark test problems which contains both connected and non‐connected graphs, study of the algebraic connectivity (λ2) of an FEG, eigensolver convergence verification, running time performance evaluation and assessment of the algorithm on a set of practical finite element examples. It is shown that the SFR algorithm is effective in reordering nodes and/or elements of generic finite element meshes. Moreover, it computes orderings which compare favourably with the ones obtained by some previous algorithms that have been published in the technical literature.
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U2 - 10.1002/nme.1620370908
DO - 10.1002/nme.1620370908
M3 - Article
AN - SCOPUS:0028436646
SN - 0029-5981
VL - 37
SP - 1531
EP - 1555
JO - International Journal for Numerical Methods in Engineering
JF - International Journal for Numerical Methods in Engineering
IS - 9
ER -