Enseñanza

Triangular grid generators for the eigenvalue calculation with edge elements

G.M. Ortigoza Capetillo*

Facultad de Ingeniería Universidad Veracruzana, Calzada Adolfo Ruiz Cortines s/n, Fracc. Costa Verde Boca del Río Ver, México, Phone (229) 921–61–21, 921–87–55123, Fax (229) 921–65–32. e–mail: *gortigoza@uv.mx

Recibido el 7 de noviembre de 2008
Aceptado el 1 de octubre de 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 of the different grid generators tested. 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: Triangular grid generators; edge elements; RCM ordering; generalized eigenproblem.

Resumen

En este trabajo investigamos algunos aspectos computacionales del cálculo de eigenvalores con elementos de borde, entre los que se incluye la importancia del generador de mallas y la numeración de nodos–lados. Como muestran los ejemplos la estructura esparcida de las matrices de masa y momento es altamente influenciada por la numeración de los lados de los diferentes generadores de mallas probados. Una reducción de ancho de banda notable puede obtenerse mediante la combinación apropiada del esquema de numeración de los lados con el método empleado por el generador de mallas. Mas aún, una renumeración como el algoritmo Reverse Cuthill–McKee puede mejorar la reducción de ancho de banda lo cual es necesario para reducir requerimientos de almacenamiento.

Descriptores: Generadores de mallas triangulares; elementos de borde; renumeración RCM; eigenproblemas generalizados.

PACS: 02.30.Jr; 02.70.Dh; 41.20.Jb

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