{"id":53050,"date":"2006-10-06T00:00:00","date_gmt":"2006-10-06T00:00:00","guid":{"rendered":"https:\/\/www.deberes.net\/tesis\/sin-categoria\/metodos-iterativos-eficientes-para-problemas-de-conveccion-difusion-transitorios\/"},"modified":"2006-10-06T00:00:00","modified_gmt":"2006-10-06T00:00:00","slug":"metodos-iterativos-eficientes-para-problemas-de-conveccion-difusion-transitorios","status":"publish","type":"post","link":"https:\/\/www.deberes.net\/tesis\/modelos-numericos-de-la-atmosfera\/metodos-iterativos-eficientes-para-problemas-de-conveccion-difusion-transitorios\/","title":{"rendered":"Metodos iterativos eficientes para problemas de conveccion-difusion transitorios"},"content":{"rendered":"<h2>Tesis doctoral de <strong> Mar\u00eda  Luisa Sandoval Solis <\/strong><\/h2>\n<p>Diversos procesos naturales e industriales de inter\u00e9s medioambiental se modelan a trav\u00e9s de la ecuaci\u00f3n de convecci\u00f3n-difusi\u00f3n-reacci\u00f3n transitoria. Dos aplicaciones tecnol\u00f3gicas que han motivado esta tesis son el funcionamiento de filtros de carb\u00f3n activo y la dispersi\u00f3n de contaminantes en la atm\u00f3sfera. Para que la modelizaci\u00f3n num\u00e9rica de estos problemas sea eficaz es indispensable contar con un solver lineal eficiente para resolver los sistemas de ecuaciones obtenidos al discretizar la ecuaci\u00f3n en derivadas parciales, mediante elementos finitos. por ello, el objetivo de esta tesis es resolver de forma eficiente los grandes sistemas de ecuaciones, sim\u00e9tricos definidos positivos (sdp), tipo sparse asociados a los problemas de convecci\u00f3n-difusi\u00f3n transitorios. Con este fin se estudian los precondicionadores tanto expl\u00edcitos como impl\u00edcitos, as\u00ed como los m\u00e9todos de descomposici\u00f3n de dominios (dd). la tesis se estructura en tres partes. En la primera se elabora un an\u00e1lisis computacional detallado del comportamiento de dos familias de factorizaciones incompletas de cholesky (fic): de memoria prescrita y de umbral. Estas t\u00e9cnicas se utilizan para precondicionar el m\u00e9todo iterativo de gradientes conjugados (pcg). En la segunda parte se construye una inversa aproximada sparse sim\u00e9trica (sspai) basada en la minimizaci\u00f3n en la norma de frobenius. El precondicionador expl\u00edcito se dise\u00f1a para resolver en paralelo grandes sistemas de ecuaciones sparse, sdp, tridiagonales por bloques con m\u00faltiples lados derechos. finalmente, se desarrolla el m\u00e9todo multiplicativo de schwarz (msm) en dominios activos, es decir, dd solapados con la innovaci\u00f3n de activar y desactivar dominios. Se estudia el comportamiento de esta estrategia al resolver los subproblemas mediante: (1) el m\u00e9todo directo de cholesky y (2) pcg + fic de umbral. de los resultados num\u00e9ricos presentados se concluye que es preferible utilizar el m\u00e9todo directo de cholesky para sistemas<\/p>\n<p>&nbsp;<\/p>\n<h3>Datos acad\u00e9micos de la tesis doctoral \u00ab<strong>Metodos iterativos eficientes para problemas de conveccion-difusion transitorios<\/strong>\u00ab<\/h3>\n<ul>\n<li><strong>T\u00edtulo de la tesis:<\/strong>\u00a0 Metodos iterativos eficientes para problemas de conveccion-difusion transitorios <\/li>\n<li><strong>Autor:<\/strong>\u00a0 Mar\u00eda  Luisa Sandoval Solis <\/li>\n<li><strong>Universidad:<\/strong>\u00a0 Polit\u00e9cnica de catalunya<\/li>\n<li><strong>Fecha de lectura de la tesis:<\/strong>\u00a0 10\/06\/2006<\/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>Antonio Rodriguez Ferran<\/li>\n<\/ul>\n<\/li>\n<li><strong>Tribunal<\/strong>\n<ul>\n<li>Presidente del tribunal: Rafael alejandro Montenegro armas <\/li>\n<li>Antonio Susin s\u00e1nchez (vocal)<\/li>\n<li>Rafael Bru Garc\u00eda (vocal)<\/li>\n<li>pedro D\u00edez mej\u00eda (vocal)<\/li>\n<\/ul>\n<\/li>\n<\/ul>\n<p>&nbsp;<\/p>\n","protected":false},"excerpt":{"rendered":"<p>Tesis doctoral de Mar\u00eda Luisa Sandoval Solis Diversos procesos naturales e industriales de inter\u00e9s medioambiental se modelan a trav\u00e9s de [&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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