<?xml version="1.0" encoding="ISO-8859-1"?><article xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink" xmlns:xsi="http://www.w3.org/2001/XMLSchema-instance">
<front>
<journal-meta>
<journal-id>2007-0705</journal-id>
<journal-title><![CDATA[Nova scientia]]></journal-title>
<abbrev-journal-title><![CDATA[Nova scientia]]></abbrev-journal-title>
<issn>2007-0705</issn>
<publisher>
<publisher-name><![CDATA[Universidad de La Salle Bajío A. C., Coordinación de Investigación]]></publisher-name>
</publisher>
</journal-meta>
<article-meta>
<article-id>S2007-07052018000100263</article-id>
<article-id pub-id-type="doi">10.21640/ns.v10i20.1317</article-id>
<title-group>
<article-title xml:lang="en"><![CDATA[Reordering edges and elements in unstructured meshes to reduce execution time in Finite Element Computations]]></article-title>
<article-title xml:lang="es"><![CDATA[Reordenando bordes y elementos en mallas no estructuradas para reducir el tiempo de ejecución en Cálculos de Elementos Finitos]]></article-title>
</title-group>
<contrib-group>
<contrib contrib-type="author">
<name>
<surname><![CDATA[Ortigoza Capetillo]]></surname>
<given-names><![CDATA[Gerardo M.]]></given-names>
</name>
<xref ref-type="aff" rid="Aff"/>
</contrib>
<contrib contrib-type="author">
<name>
<surname><![CDATA[Lorandi Medina]]></surname>
<given-names><![CDATA[Alberto P.]]></given-names>
</name>
<xref ref-type="aff" rid="Aff"/>
</contrib>
<contrib contrib-type="author">
<name>
<surname><![CDATA[García Reynoso]]></surname>
<given-names><![CDATA[Alfonso C.]]></given-names>
</name>
<xref ref-type="aff" rid="Aff"/>
</contrib>
</contrib-group>
<aff id="Af1">
<institution><![CDATA[,Universidad Veracruzana Facultad de Ingeniería ]]></institution>
<addr-line><![CDATA[Boca del Rio ]]></addr-line>
<country>Mexico</country>
</aff>
<aff id="Af2">
<institution><![CDATA[,Universidad Veracruzana Instituto de Ingeniería ]]></institution>
<addr-line><![CDATA[Boca del Río ]]></addr-line>
<country>Mexico</country>
</aff>
<pub-date pub-type="pub">
<day>00</day>
<month>00</month>
<year>2018</year>
</pub-date>
<pub-date pub-type="epub">
<day>00</day>
<month>00</month>
<year>2018</year>
</pub-date>
<volume>10</volume>
<numero>20</numero>
<fpage>263</fpage>
<lpage>279</lpage>
<copyright-statement/>
<copyright-year/>
<self-uri xlink:href="http://www.scielo.org.mx/scielo.php?script=sci_arttext&amp;pid=S2007-07052018000100263&amp;lng=en&amp;nrm=iso"></self-uri><self-uri xlink:href="http://www.scielo.org.mx/scielo.php?script=sci_abstract&amp;pid=S2007-07052018000100263&amp;lng=en&amp;nrm=iso"></self-uri><self-uri xlink:href="http://www.scielo.org.mx/scielo.php?script=sci_pdf&amp;pid=S2007-07052018000100263&amp;lng=en&amp;nrm=iso"></self-uri><abstract abstract-type="short" xml:lang="en"><p><![CDATA[Abstract: Reverse Cuthill McKee (RCM) reordering can be applied to either edges or elements of unstructured meshes (triangular/tetrahedral), in accordance to the respective finite element formulation, to reduce the bandwidth of stiffness matrices. Grid generators are mainly designed for nodal based finite elements. Their output is a list of nodes (2d or 3d) and an array describing element connectivity, be it triangles or tetrahedrons. However, for edge-defined finite element formulations a numbering of the edges is required. Observations are reported for Triangle/Tetgen Delaunay grid generators and for the sparse structure of the assembled matrices in both edge- and element-defined formulations. The RCM is a renumbering algorithm traditionally applied to the nodal graph of the mesh. Thus, in order to apply this renumbering to either the edges or the elements of the respective finite element formulation, graphs of the mesh were generated. Significant bandwidth reduction was obtained. This translates to reduction in the execution effort of the sparse-matrix-times-vector product. Compressed Sparse Row format was adopted and the matrix-times-vector product was implemented in an OpenMp parallel routine.]]></p></abstract>
<abstract abstract-type="short" xml:lang="es"><p><![CDATA[Resumen: En este trabajo mostramos cómo el reordenamiento RCM puede aplicarse a los lados y a los elementos de una malla no estructurada (tetraedros/triángulos) para reducir el ancho de banda de las matrices de esfuerzos para las formulaciones de elementos finitos definidas sobre lados o sobre elementos. Los generadores de malla han sido diseñados principalmente para elementos finitos nodales, sus salidas son una lista de nodos (2d/3d) y un arreglo de la conectividad de los elementos (triángulos/tetraedros). Sin embargo, para las formulaciones de elementos finitos basados en los lados se requiere una enumeración de los lados de la malla. Reportamos observaciones realizadas con los generadores de mallas Triangle y Tetgen y las estructuras esparcidas de las matrices de esfuerzos obtenidas en formulaciones sobre los lados y sobre elementos. El RCM es un algoritmo de re-enumeración tradicionalmente aplicado a los nodos de la malla. Así para aplicar este algoritmo de re-enumeración al caso de elementos finitos sobre lados y elementos, definimos los grafos de los lados y el grafo de los elementos. Obtenemos así una noTable reducción de ancho de banda de las matrices de esfuerzos, lo que se traduce en reducción de tiempo de ejecución en la multiplicación de matrices esparcidas por un vector. Usamos matrices comprimidas por filas e implementamos la multiplicación de matriz esparcida por vector en una rutina en paralelo usando OpenMp.]]></p></abstract>
<kwd-group>
<kwd lng="en"><![CDATA[RCM reordering]]></kwd>
<kwd lng="en"><![CDATA[finite element]]></kwd>
<kwd lng="en"><![CDATA[bandwidth reduction of stiffness matrices]]></kwd>
<kwd lng="en"><![CDATA[edge and element graphs of the mesh]]></kwd>
<kwd lng="es"><![CDATA[re-enumeración de lados y elementos]]></kwd>
<kwd lng="es"><![CDATA[formulación de elementos finitos]]></kwd>
<kwd lng="es"><![CDATA[reducción de ancho de banda y tiempo de ejecución]]></kwd>
<kwd lng="es"><![CDATA[matriz esparcida por vector]]></kwd>
</kwd-group>
</article-meta>
</front><back>
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