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Computación y Sistemas

Print version ISSN 1405-5546

Comp. y Sist. vol.14 n.1 México Jul./Sep. 2010

 

Artículos

 

Tetrahedral Grid Generators and the Eigenvalue Calculation with Edge Elements

 

Generadores de malla tetraédricos y el cálculo de Eigenvalores con elementos de contorno

 

Gerardo Mario Ortigoza Capetillo

 

Facultad de Ingeniería Universidad Veracruzana Calzada Adolfo Ruiz Cortines s/n, Fracc. Costa Verde Boca del Río Ver, México. E–mail: gortigoza@uv.mx

 

Article received on September 03, 2008
Accepted on February 25, 2009

 

Abstract

In this work we investigate some computational aspects of the eigenvalue calculation with edge elements; those include: the importance of the grid generator and node–edge numbering. As the examples show, the sparse structure of the mass and stiffness matrices is highly influenced by the edge numbering.

Tetrahedral grid generators are mainly designed for nodal based finite elements so an edge numbering is required. Two different edge numbering schemes are tested with six different grid generators. Significant bandwidth reduction can be obtained by the proper combination of the edge numbering scheme with the grid generator method. Moreover, an ordering algorithm such as the Reverse Cuthill McKee can improve the bandwidth reduction which is necessary to reduce storage requirements.

Keywords: Tetrahedral grid generators, edge elements, RCM ordering, generalized eigenproblem.

 

Resumen

En este trabajo se investigan algunos aspectos computacionales del cálculo de eigenvalores con elementos de contorno tales como la importancia del generador de mallas y la numeración de nodos y lados. Como muestran los ejemplos, la estructura esparcida de las matrices de masa y momentos es altamente influenciada por la numeración de los lados.

Generadores de mallas en tetraedros son diseñados principalmente para elementos finitos basados en los nodos, así una numeración de los lados es requerida. Se realizaron pruebas con dos esquemas de enumeración de los lados con seis generadores de mallas distintos. Una reducción de banda significante puede obtenerse con una combinación apropiada de esquema de numeración de los lados con el método empleado por el generador de malla. Más aún un algoritmo de reordenamiento como el RCM puede mejorar la reducción de ancho de banda lo cual es necesario para reducir los requerimientos de almacenamiento.

Palabras Clave: Generadores de mallas en tetraedros, elementos de contorno, reordenamientos RCM, valores propios generalizados.

 

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