{"id":86182,"date":"2018-03-10T00:10:42","date_gmt":"2018-03-10T00:10:42","guid":{"rendered":"https:\/\/www.deberes.net\/tesis\/sin-categoria\/metodos-numericos-para-la-resolucion-de-la-ecuacion-de-la-difusion-neutronica-dependiente-del-tiempo\/"},"modified":"2018-03-10T00:10:42","modified_gmt":"2018-03-10T00:10:42","slug":"metodos-numericos-para-la-resolucion-de-la-ecuacion-de-la-difusion-neutronica-dependiente-del-tiempo","status":"publish","type":"post","link":"https:\/\/www.deberes.net\/tesis\/matematicas\/metodos-numericos-para-la-resolucion-de-la-ecuacion-de-la-difusion-neutronica-dependiente-del-tiempo\/","title":{"rendered":"M\u00e9todos num\u00e9ricos para la resoluci\u00f3n de la ecuaci\u00f3n de la difusi\u00f3n neutr\u00f3nica dependiente del tiempo."},"content":{"rendered":"<h2>Tesis doctoral de <strong> Jos\u00e9 Mar\u00edn Mateos-aparicio <\/strong><\/h2>\n<p>La simulaci\u00f3n del comportamiento din\u00e1mico de la poblaci\u00f3n neutr\u00f3nica en el n\u00facleo de un reactor nuclear se realiza mediante la ecuaci\u00f3n de la difusi\u00f3n neutr\u00f3ncia dependiente del tiempo. La forma t\u00edpica de abordar el problema es dicretizando tanto la parte espacial como la parte temporal de la ecuaci\u00f3n de la difusi\u00f3n neutr\u00f3nica.  se presentan y comparan diferentes m\u00e9todos para la discretizaci\u00f3n de la parte espacial de esta ecuaci\u00f3n.Concretamente el m\u00e9todo de las diferencias finitas centradas y un m\u00e9todo de colocaci\u00f3n nodal basado en la expansi\u00f3n del flujo neutr\u00f3nicao en t\u00e9rminos de polinomiso ortonormales de legendre.  tras discretizar la ecuaci\u00f3n se obtienen sistemas de ecuaciones lineales de gran tama\u00f1o y fundamentalmente vac\u00edos que hay que resolver en cada paso de tiempo de integraci\u00f3n. Es el objetivo fundamental de la tesis el estudio de diferentes m\u00e9todos iterativos para resolver estos sistemas de ecuaciones lineales.  se estudian las propiedades de convergencia de m\u00e9todos iterativos estacionarios por bloques de segundo grado para la soluci\u00f3n de sistemas de ecuaciones lineales, complet\u00e1ndose con un estudio experimental mediante la simulaci\u00f3n de transitorios 2d y 3d que han permitido comparar los diferentes m\u00e9todos que se proponen.  se presenta una t\u00e9cnica variacional para acelerar la convergencia de los m\u00e9todos estacionarios de segundo grado presentados. Esta t\u00e9cnica consiste en un m\u00e9todo de minimizaci\u00f3n del residuo en un subespacio bidimensional. los experimentos num\u00e9ricos muestran que esta t\u00e9cnica permite mejorar sustancialmente la velocidad de convergencia de los m\u00e9todos de segundo grado. Adem\u00e1s, los m\u00e9todos de segundo grado acelerados se comparan con otros m\u00e9todos basados en subespacios de krylov (bicgstab, gmres(k) y tfqmr mostrando ser competitivos frente a estos.  finalmente, se proponen algoritmos multinivel que permitan disminuir el tiempo de simulaci\u00f3n cuando se utiliza un n\u00fam<\/p>\n<p>&nbsp;<\/p>\n<h3>Datos acad\u00e9micos de la tesis doctoral \u00ab<strong>M\u00e9todos num\u00e9ricos para la resoluci\u00f3n de la ecuaci\u00f3n de la difusi\u00f3n neutr\u00f3nica dependiente del tiempo.<\/strong>\u00ab<\/h3>\n<ul>\n<li><strong>T\u00edtulo de la tesis:<\/strong>\u00a0 M\u00e9todos num\u00e9ricos para la resoluci\u00f3n de la ecuaci\u00f3n de la difusi\u00f3n neutr\u00f3nica dependiente del tiempo. <\/li>\n<li><strong>Autor:<\/strong>\u00a0 Jos\u00e9 Mar\u00edn Mateos-aparicio <\/li>\n<li><strong>Universidad:<\/strong>\u00a0 Polit\u00e9cnica de Valencia<\/li>\n<li><strong>Fecha de lectura de la tesis:<\/strong>\u00a0 26\/07\/2000<\/li>\n<\/ul>\n<p>&nbsp;<\/p>\n<h3>Direcci\u00f3n y tribunal<\/h3>\n<ul>\n<li><strong>Director de la tesis<\/strong>\n<ul>\n<li>Rafael Bru Carg\u00eda<\/li>\n<\/ul>\n<\/li>\n<li><strong>Tribunal<\/strong>\n<ul>\n<li>Presidente del tribunal: gumersindo Verdu martin <\/li>\n<li>violeta Migallon gomis (vocal)<\/li>\n<li>cristina Corral ortega (vocal)<\/li>\n<li>Jos\u00e9 Penades Martinez (vocal)<\/li>\n<\/ul>\n<\/li>\n<\/ul>\n<p>&nbsp;<\/p>\n","protected":false},"excerpt":{"rendered":"<p>Tesis doctoral de Jos\u00e9 Mar\u00edn Mateos-aparicio La simulaci\u00f3n del comportamiento din\u00e1mico de la poblaci\u00f3n neutr\u00f3nica en el n\u00facleo de un [&hellip;]<\/p>\n","protected":false},"author":1,"featured_media":0,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"site-sidebar-layout":"default","site-content-layout":"","ast-site-content-layout":"","site-content-style":"default","site-sidebar-style":"default","ast-global-header-display":"","ast-banner-title-visibility":"","ast-main-header-display":"","ast-hfb-above-header-display":"","ast-hfb-below-header-display":"","ast-hfb-mobile-header-display":"","site-post-title":"","ast-breadcrumbs-content":"","ast-featured-img":"","footer-sml-layout":"","theme-transparent-header-meta":"","adv-header-id-meta":"","stick-header-meta":"","header-above-stick-meta":"","header-main-stick-meta":"","header-below-stick-meta":"","astra-migrate-meta-layouts":"default","ast-page-background-enabled":"default","ast-page-background-meta":{"desktop":{"background-color":"var(--ast-global-color-4)","background-image":"","background-repeat":"repeat","background-position":"center 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