<?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>0122-5383</journal-id>
<journal-title><![CDATA[CT&F - Ciencia, Tecnología y Futuro]]></journal-title>
<abbrev-journal-title><![CDATA[C.T.F Cienc. Tecnol. Futuro]]></abbrev-journal-title>
<issn>0122-5383</issn>
<publisher>
<publisher-name><![CDATA[Instituto Colombiano del Petróleo (ICP) - ECOPETROL S.A.]]></publisher-name>
</publisher>
</journal-meta>
<article-meta>
<article-id>S0122-53832019000200015</article-id>
<article-id pub-id-type="doi">10.29047/01225383.178</article-id>
<title-group>
<article-title xml:lang="en"><![CDATA[OPTIMAL SHAPE PARAMETER FOR MESHLESS SOLUTION OF THE 2D HELMHOLTZ EQUATION]]></article-title>
<article-title xml:lang="es"><![CDATA[PARAMETRO OPTIMO DE FORMA PARA LA SOLUCIÓN DE LA ECUACIÓN DE HELMHOLTZ 2D EN MODELO SIN MALLA]]></article-title>
</title-group>
<contrib-group>
<contrib contrib-type="author">
<name>
<surname><![CDATA[Londoño]]></surname>
<given-names><![CDATA[Mauricio-A]]></given-names>
</name>
<xref ref-type="aff" rid="Aff"/>
</contrib>
<contrib contrib-type="author">
<name>
<surname><![CDATA[Montegranario]]></surname>
<given-names><![CDATA[Hebert,]]></given-names>
</name>
<xref ref-type="aff" rid="Aff"/>
</contrib>
</contrib-group>
<aff id="Af1">
<institution><![CDATA[,Universidad de Antioquia Instituto de Matematicas ]]></institution>
<addr-line><![CDATA[Medellin ]]></addr-line>
<country>Colombia</country>
</aff>
<pub-date pub-type="pub">
<day>00</day>
<month>12</month>
<year>2019</year>
</pub-date>
<pub-date pub-type="epub">
<day>00</day>
<month>12</month>
<year>2019</year>
</pub-date>
<volume>9</volume>
<numero>2</numero>
<fpage>15</fpage>
<lpage>35</lpage>
<copyright-statement/>
<copyright-year/>
<self-uri xlink:href="http://www.scielo.org.co/scielo.php?script=sci_arttext&amp;pid=S0122-53832019000200015&amp;lng=en&amp;nrm=iso"></self-uri><self-uri xlink:href="http://www.scielo.org.co/scielo.php?script=sci_abstract&amp;pid=S0122-53832019000200015&amp;lng=en&amp;nrm=iso"></self-uri><self-uri xlink:href="http://www.scielo.org.co/scielo.php?script=sci_pdf&amp;pid=S0122-53832019000200015&amp;lng=en&amp;nrm=iso"></self-uri><abstract abstract-type="short" xml:lang="en"><p><![CDATA[ABSTRACT The solution of the Helmholtz equation is a fundamental step in frequency domain seismic imaging. This paper deals with a numerical study of solutions for 2D Helmholtz equation using a Gaussian radial basis function-generated finite difference scheme (RBFFD). We analyze the behavior of the local truncation error in approximating partial derivatives of the 2D Helmholtz equation solutions when the shape parameter of RBF varies. For discretization, we performed, by means of a classical numerical dispersion analysis with plane waves, a minimization of the error function to obtain local and adaptive near optimal shape parameters according to the local wavelength of the required solution. In particular, the method is applied to obtain a simple and accurate solver by using stencils which seven nodes on hexagonal regular grids, wich mitigate pollution-effects. We validated numerically that the stability and isotropy are enhanced with respect to Cartesian grids. Our method is tested with standard case studies and velocity models, showing similar or better accuracy than finite difference and finite element methods. This is an efficient way for interacting with inverse and imaging problems such as Full Wave Inversion]]></p></abstract>
<abstract abstract-type="short" xml:lang="es"><p><![CDATA[RESUMEN La solución de la ecuación de Helmholtz es una parte fundamental en la modelación sísmica en el dominio de la frecuencia. Este artículo realiza un análisis numérico de las soluciones de la ecuación de Helmholtz 2D utilizando un esquema de diferencias finitas (RBFFD), generado por funciones gaussianas de Base radial. Se analiza el comportamiento del error de truncamiento local al aproximar las derivadas parciales de las soluciones de la ecuación de Helmholtz 2D cuando varía el parámetro de forma de la RBF. Para la discretización, hemos realizado, mediante un análisis de dispersión clásico con ondas planas , una optimización de la función de error para obtener valores locales y adaptativos del parámetro de forma de acuerdo con la longitud de onda local de la solución requerida. En particular, el método se aplica para obtener un programa sencillo y óptimo usando plantillas de siete nodos sobre mallas regulares hexagonales, que mitigan el efecto polución. Se comprueba numéricamente que la estabilidad e isotropía son mejoradas con respecto a las mallas cartesianas. Nuestro método es probado con casos de estudio y modelos de velocidad estándar, mostrando exactitud similar o mejor que los métodos de diferencias o elemento finitos. Esta es una manera eficiente de interactuar con problemas inverso y de imagen tales como la inversión de onda completa]]></p></abstract>
<kwd-group>
<kwd lng="en"><![CDATA[RBF-FD]]></kwd>
<kwd lng="en"><![CDATA[Helmholtz equation]]></kwd>
<kwd lng="en"><![CDATA[Shape parameter]]></kwd>
<kwd lng="en"><![CDATA[pollution effect]]></kwd>
<kwd lng="es"><![CDATA[RBFFD]]></kwd>
<kwd lng="es"><![CDATA[Ecuación de Helmholtz]]></kwd>
<kwd lng="es"><![CDATA[Parámetro de forma]]></kwd>
<kwd lng="es"><![CDATA[Efecto polución]]></kwd>
</kwd-group>
</article-meta>
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