<?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>0185-1101</journal-id>
<journal-title><![CDATA[Revista mexicana de astronomía y astrofísica]]></journal-title>
<abbrev-journal-title><![CDATA[Rev. mex. astron. astrofis]]></abbrev-journal-title>
<issn>0185-1101</issn>
<publisher>
<publisher-name><![CDATA[Universidad Nacional Autónoma de México, Instituto de Astronomía]]></publisher-name>
</publisher>
</journal-meta>
<article-meta>
<article-id>S0185-11012022000200197</article-id>
<article-id pub-id-type="doi">10.22201/ia.01851101p.2022.58.02.03</article-id>
<title-group>
<article-title xml:lang="en"><![CDATA[Assessing the Hierarchical Hamiltonian Splitting Integrator for Collisionless N -Body Simulations]]></article-title>
</title-group>
<contrib-group>
<contrib contrib-type="author">
<name>
<surname><![CDATA[Aguilar-Argüello]]></surname>
<given-names><![CDATA[G.]]></given-names>
</name>
<xref ref-type="aff" rid="Aff"/>
</contrib>
<contrib contrib-type="author">
<name>
<surname><![CDATA[Valenzuela]]></surname>
<given-names><![CDATA[O.]]></given-names>
</name>
<xref ref-type="aff" rid="Aff"/>
</contrib>
<contrib contrib-type="author">
<name>
<surname><![CDATA[Velázquez]]></surname>
<given-names><![CDATA[H.]]></given-names>
</name>
<xref ref-type="aff" rid="Aff"/>
</contrib>
<contrib contrib-type="author">
<name>
<surname><![CDATA[Clemente]]></surname>
<given-names><![CDATA[J. C.]]></given-names>
</name>
<xref ref-type="aff" rid="Aff"/>
</contrib>
<contrib contrib-type="author">
<name>
<surname><![CDATA[Trelles]]></surname>
<given-names><![CDATA[J. A.]]></given-names>
</name>
<xref ref-type="aff" rid="Aff"/>
</contrib>
</contrib-group>
<aff id="Af1">
<institution><![CDATA[,Universidad Nacional Autónoma de México Instituto de Astronomía ]]></institution>
<addr-line><![CDATA[México CDMX]]></addr-line>
<country>Mexico</country>
</aff>
<pub-date pub-type="pub">
<day>00</day>
<month>00</month>
<year>2022</year>
</pub-date>
<pub-date pub-type="epub">
<day>00</day>
<month>00</month>
<year>2022</year>
</pub-date>
<volume>58</volume>
<numero>2</numero>
<fpage>197</fpage>
<lpage>213</lpage>
<copyright-statement/>
<copyright-year/>
<self-uri xlink:href="http://www.scielo.org.mx/scielo.php?script=sci_arttext&amp;pid=S0185-11012022000200197&amp;lng=en&amp;nrm=iso"></self-uri><self-uri xlink:href="http://www.scielo.org.mx/scielo.php?script=sci_abstract&amp;pid=S0185-11012022000200197&amp;lng=en&amp;nrm=iso"></self-uri><self-uri xlink:href="http://www.scielo.org.mx/scielo.php?script=sci_pdf&amp;pid=S0185-11012022000200197&amp;lng=en&amp;nrm=iso"></self-uri><abstract abstract-type="short" xml:lang="en"><p><![CDATA[ABSTRACT The large dynamic range in some astrophysical N-body problems led to the use of adaptive multi-time-steps; however, the search for optimal strategies is still challenging. We numerically quantify the performance of the hierarchical Hamiltonian Splitting (HHS) integrator for collisionless simulations using a direct summation code. We compare HHS with the constant global time-step leapfrog integrator, and with the adaptive one (AKDK). We find that HHS is approximately reversible, whereas AKDK is not. Therefore, it is possible to find a combination of parameters such that the energy drift is considerably milder for HHS, resulting in a better performance. We conclude that HHS is an attractive alternative to AKDK, and it is certainly advantageous for direct summation and P3M codes. Also, we find advantages with GADGET4 (Tree/FMM) HHS implementation that are worth exploring further.]]></p></abstract>
<abstract abstract-type="short" xml:lang="es"><p><![CDATA[RESUMEN El gran intervalo dinámico en algunos problemas astrofísicos de N-cuerpos ha llevado al uso de pasos de tiempo múltiples adaptivos, sin embargo, la búsqueda de estrategias óptimas es aún un reto. Estudiamos numéricamente el integrador Hierarchical Hamiltonian Splitting (HHS) utilizando un código de suma directa y comparamos con el rendimiento de leapfrog con paso global constante y su versión multi-paso adaptivo (AKDK). Encontramos que HHS es aproximadamente reversible, mientras que AKDK no. Por lo que es posible encontrar una combinación de parámetros tales que el cambio de energía es considerablemente menor para HHS, resultando en una mayor eficiencia. Concluimos que HHS es una alternativa competitiva con ventaja para códigos de suma directa y P3M. También, hallamos ventajas para la implementación de HHS en GADGET4 (Árbol/FMM) que merecen ser investigadas más.]]></p></abstract>
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