Título: | RESEQUENCING TECHNIQUES FOR SOLVING LARGE SPARSE SYSTEMS | ||||||||||||
Autor: |
IVAN FABIO MOTA DE MENEZES |
||||||||||||
Colaborador(es): |
MARCELO GATTASS - Orientador |
||||||||||||
Catalogação: | 26/JUL/2002 | Língua(s): | PORTUGUESE - BRAZIL |
||||||||||
Tipo: | TEXT | Subtipo: | THESIS | ||||||||||
Notas: |
[pt] Todos os dados constantes dos documentos são de inteira responsabilidade de seus autores. Os dados utilizados nas descrições dos documentos estão em conformidade com os sistemas da administração da PUC-Rio. [en] All data contained in the documents are the sole responsibility of the authors. The data used in the descriptions of the documents are in conformity with the systems of the administration of PUC-Rio. |
||||||||||||
Referência(s): |
[pt] https://www.maxwell.vrac.puc-rio.br/projetosEspeciais/ETDs/consultas/conteudo.php?strSecao=resultado&nrSeq=2779&idi=1 [en] https://www.maxwell.vrac.puc-rio.br/projetosEspeciais/ETDs/consultas/conteudo.php?strSecao=resultado&nrSeq=2779&idi=2 |
||||||||||||
DOI: | https://doi.org/10.17771/PUCRio.acad.2779 | ||||||||||||
Resumo: | |||||||||||||
This work presents resequencing techniques for minimizing
bandwidth, profile and wavefront of finite element meshes.
A unified approach relating a finite element mesh, its
associated graphs, and the corresponding matrices is
proposed. The geometrical information available from
conventional finite element program is also used in order
to improve heuristic algorithms. Following these ideas,
the algorithms are classified here as a nodal graph (G), a
dual graph (G) or a communication graph (G.) associated
with a generic finie element mesh. The most widely used
topological algorithms, such as Reverse-Cuthill-McKee
(RCM), Collins, Gibbs-Poole-Stockmeyer (GPS), Gibbs-King
(GK), Snay, and Sloan, are investigated in detail. In
particular, the Collins algorithm is extended to consider
nonconnected components in associated graph and the
ordering provide by this algorithm is reverted for
improved profile. This new version is called Modified
Reverse Collins (MRCollins). A purely geometrical
algorithm, called Coordinate Based Bandwidth and Profile
Reduction (CBBPR), is presented. A new hybrid reordering
algorithm (HybWP) for wavefront and profile reduction is
proposed. The Laplacian matrix [L(G), L(G) or L(G.)],
used for the study of spectral properties of an FEG, is
constructed from usual vertex and edge conectivities of a
graph. An automatic algorithm, based on spectral
properties of an FEG, is proposed to reorder the nodes
and/or elements of the associated finite element meshes.
The new algorithm, called Spectral FEG Resequencing (SFR),
uses global information in the graph; it does not depende
on a pseudoperipheral vertex in the resequencing process;
and it does not use any kind of level structure of the
graph. A new spectral algorithm for finding
pseudoperipheral vertices in graphs is also proposed. The
algorithmpresented herein are computationally implemented
and tested against several numerical examples. Finally,
conclusions are drawn and directions for futue work are
given.
|
|||||||||||||
|