BANDWIDTH REDUCTION ON SPARSE MATRICES BY INTRODUCING NEW VARIABLES.

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Bibliographic Details
Title:	BANDWIDTH REDUCTION ON SPARSE MATRICES BY INTRODUCING NEW VARIABLES.
Alternate Title:	REDUCCIÓN DEL ANCHO DE BANDA DE MATRICES DISPERSAS MEDIANTE LA INTRODUCCIÓN DE NUEVAS VARIABLES.
Authors:	Glüge, Rainer¹ gluege@ovgu.de
Source:	INGENIARE - Revista Chilena de Ingeniería. 2010, Vol. 18 Issue 3, p395-400. 6p. 1 Diagram, 1 Chart.
Subjects:	Sparse matrix software, Finite element method, Mathematical optimization, Linear systems, Asymptotic homogenization
Abstract (English):	A sparse matrix bandwidth reduction method is analyzed. It consists of equation splitting, substitution and introducing new variables, similar to the substructure decomposition in the finite element method (FEM). It is especially useful when the bandwidth cannot be reduced by strategically interchanging columns and rows. In such cases, equation splitting and successive reordering can further reduce the bandwidth, at cost of introducing new variables. While the substructure decomposition is carried out before the system matrix is built, the given approach is applied afterwards, independently on the origin of the linear system. It is successfully applied to a sparse matrix, the bandwidth of which cannot be reduced by reordering. For the exemplary FEM simulation, an increase of performance of the direct solver is obtaine. [ABSTRACT FROM AUTHOR]
Abstract (Spanish):	Se analiza un método para la reducción del ancho de banda de matrices dispersas, el cual consiste en fraccionar ecuaciones, substituir e introducir nuevas variables, similar a la descomposición en subestructuras utilizada en el método de los elementos finitos (FEM). Es especialmente útil si el ancho de banda no puede ser reducido intercambiando estratégicamente columnas y líneas. En estos casos, dividir ecuaciones y reordenar líneas y columnas puede reducir el ancho de banda, al costo de introducir nuevas variables. En comparación con el método de las subestructuras en el FEM, en el cual la descomposición está hecha antes de obtener la matriz del sistema, la metodología que se presenta está aplicada después de obtener el sistema lineal, independiente de su origen. El método está aplicado con éxito en una matriz dispersa en el contexto del FEM, lo cual resulta en un aumento de eficiencia del algoritmo directo para resolver el sistema lineal. [ABSTRACT FROM AUTHOR]
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Database:	Engineering Source

Description
Abstract:	A sparse matrix bandwidth reduction method is analyzed. It consists of equation splitting, substitution and introducing new variables, similar to the substructure decomposition in the finite element method (FEM). It is especially useful when the bandwidth cannot be reduced by strategically interchanging columns and rows. In such cases, equation splitting and successive reordering can further reduce the bandwidth, at cost of introducing new variables. While the substructure decomposition is carried out before the system matrix is built, the given approach is applied afterwards, independently on the origin of the linear system. It is successfully applied to a sparse matrix, the bandwidth of which cannot be reduced by reordering. For the exemplary FEM simulation, an increase of performance of the direct solver is obtaine. [ABSTRACT FROM AUTHOR]
ISSN:	07183291