{"id":660,"date":"2020-03-03T21:08:21","date_gmt":"2020-03-04T00:08:21","guid":{"rendered":"http:\/\/blog.ufes.br\/isaacsantos\/?page_id=660"},"modified":"2020-03-03T22:16:58","modified_gmt":"2020-03-04T01:16:58","slug":"metodos-numericos-ii-2020-1","status":"publish","type":"page","link":"https:\/\/blog.ufes.br\/isaacsantos\/ensino\/metodos-numericos-ii-2020-1\/","title":{"rendered":"M\u00e9todos Num\u00e9ricos II &#8211; 2020\/1"},"content":{"rendered":"\n<h1 class=\"wp-block-heading\"><strong>Objetivo da disciplina<\/strong>:<\/h1>\n\n\n\n<ul class=\"wp-block-list\"><li> Estudar de forma introdut\u00f3ria os m\u00e9todos de diferen\u00e7as finitas e elementos finitos para solu\u00e7\u00e3o de modelos matem\u00e1ticos baseados  em equa\u00e7\u00f5es diferenciais parciais<\/li><\/ul>\n\n\n\n<h1 class=\"wp-block-heading\"><strong>Cursos<\/strong>:<\/h1>\n\n\n\n<ul class=\"wp-block-list\"><li>Matem\u00e1tica Industrial<\/li><\/ul>\n\n\n\n<h1 class=\"wp-block-heading\"><strong>Hor\u00e1rio das aulas<\/strong>:<\/h1>\n\n\n\n<ul class=\"wp-block-list\"><li>quartas 09:00 &#8211; 11:00&nbsp; (Sala 11 &#8211; Eixo 1) e quintas 11:00 &#8211; 13:00 (Sala 15 &#8211; Eixo 3)<\/li><\/ul>\n\n\n\n<h2 class=\"wp-block-heading\"><strong>Programa da disciplina<\/strong>:<\/h2>\n\n\n\n<ol class=\"wp-block-list\"><li><strong>Revis\u00e3o dos M\u00e9todos iterativos n\u00e3o estacion\u00e1rios para sistemas lineares<\/strong> (08 aulas) <ol><li>M\u00e9todo dos Gradientes Conjugados<\/li><li>M\u00e9todo dos Gradiente Conjugados Precondicionado<\/li><li>M\u00e9todo GMRES (<em>Gereralized Minimal Residual Method<\/em>)<\/li><li>M\u00e9todo GMRES Precondicionado <\/li><\/ol><\/li><li><strong>Diferen\u00e7as Finitas: EDPs el\u00edpticas<\/strong> (14 aulas) <ol><li>A equa\u00e7\u00e3o de Laplace<\/li><li>T\u00e9cnicas de solu\u00e7\u00e3o<\/li><li>Condi\u00e7\u00f5es de contorno<\/li><li>A equa\u00e7\u00e3o de transporte Difusivo-Convectivo-Reativo<\/li><\/ol><\/li><li><strong>Diferen\u00e7as Finitas: EDPs parab\u00f3licas<\/strong> (16 aulas) <ol><li>A equa\u00e7\u00e3o do calor<\/li><li>M\u00e9todos expl\u00edcitos<\/li><li>M\u00e9todos impl\u00edcitos<\/li><li>Os m\u00e9todos de Crank-Nicolson e BDF2<\/li><li>An\u00e1lise de erro<\/li><li>Equa\u00e7\u00f5es parab\u00f3licas em duas dimens\u00f5es espaciais<\/li><\/ol><\/li><li><strong>M\u00e9todo de Elementos Finitos<\/strong> (MEF) (16 aulas) <ol><li>A abordagem geral<\/li><li>Aplica\u00e7\u00e3o do MEF a problemas unidimensionais<\/li><li>Aplica\u00e7\u00e3o do MEF a problemas bidimensionais<\/li><li>Introdu\u00e7\u00e3o ao FreeFem++<\/li><\/ol><\/li><li><strong>M\u00e9todo de Volumes Finitos<\/strong> (MVF) (06 aulas) <ol><li>Introdu\u00e7\u00e3o ao MVF <\/li><\/ol><\/li><\/ol>\n\n\n\n<h1 class=\"wp-block-heading\">Metodologia de ensino:<\/h1>\n\n\n\n<p>Aulas expositivas e de exerc\u00edcios, laborat\u00f3rio e uso de ferramentas computacionais.<\/p>\n\n\n\n<h1 class=\"wp-block-heading\">Sistema de Avalia\u00e7\u00e3o:<\/h1>\n\n\n\n<p>Ser\u00e3o aplicados duas provas parciais, dois trabalhos computacionais e atividades extras<\/p>\n\n\n\n<h1 class=\"wp-block-heading\">Datas das provas e da entrega dos trabalhos computacionais:<\/h1>\n\n\n\n<ul class=\"wp-block-list\"><li><em>Prova 1<\/em>: dia <strong>23 de abril de 2020<\/strong><\/li><li><em>Prova 2<\/em>: dia <strong>02 de julho de 2020<\/strong><\/li><li>Trabalho1: <\/li><li>Trabalho2: <\/li><li>Prova final: <strong>15 de julho de 2020<\/strong><\/li><\/ul>\n\n\n\n<h1 class=\"wp-block-heading\">Acesso \u00e0s&nbsp;aulas&nbsp;para alunos n\u00e3o matriculados na disciplina<\/h1>\n\n\n\n<h1 class=\"wp-block-heading\">C\u00e1lculo da m\u00e9dia semestral:<\/h1>\n\n\n\n<p>A m\u00e9dia semestral (MS) ser\u00e1 dada por<\/p>\n\n\n\n<p>MS = [(P1 + P2)*(0.7\/2) + (T1 + T2 + E)*(0.3\/3)],<\/p>\n\n\n\n<p>onde P1 e P2 s\u00e3o as notas das duas provas, T1 e T2 s\u00e3o as notas dos dois trabalhos computacionais e E corresponde \u00e0 notas extras (listas de exerc\u00edcios e outras atividades, a crit\u00e9rio do professor). O aluno ser\u00e1 aprovado sem necessidade de fazer a prova final se MS &gt;= 7.0.<\/p>\n\n\n\n<p>Para os alunos que far\u00e3o a prova final, a M\u00e9dia Final (MF) ser\u00e1<\/p>\n\n\n\n<p>MF = (MS + PF) \/ 2,<\/p>\n\n\n\n<p>onde PF \u00e9 a nota da prova final. O aluno ser\u00e1 aprovado se MF &gt;= 5.0.<\/p>\n\n\n\n<h1 class=\"wp-block-heading\">Software<\/h1>\n\n\n\n<h1 class=\"wp-block-heading\">Software e Linguagens de programa\u00e7\u00e3o<\/h1>\n\n\n\n<ol class=\"wp-block-list\"><li><a rel=\"noreferrer noopener\" href=\"https:\/\/www.mathworks.com\/help\/pde\/?requestedDomain=www.mathworks.com\" target=\"_blank\">Matlab (PDE-tool box)<\/a> ou <a rel=\"noreferrer noopener\" href=\"https:\/\/www.gnu.org\/software\/octave\/\" target=\"_blank\">Octave<\/a> <\/li><li><a href=\"https:\/\/www.python.org\/\">Python<\/a><\/li><li><a rel=\"noreferrer noopener\" href=\"http:\/\/www.freefem.org\/\" target=\"_blank\">FreeFem++<\/a><\/li><li><a rel=\"noreferrer noopener\" href=\"https:\/\/fenicsproject.org\/\" target=\"_blank\">Fenics<\/a><\/li><\/ol>\n\n\n\n<h1 class=\"wp-block-heading\">Links interessantes<\/h1>\n\n\n\n<ol class=\"wp-block-list\"><li><a href=\"http:\/\/persson.berkeley.edu\/distmesh\/\">DistMesh &#8211; A Simple Mesh Generator in MATLAB<\/a><\/li><li><a href=\"http:\/\/Per-Olof Persson, UC Berkeley Mathematics\" target=\"_blank\" rel=\"noreferrer noopener\">Filmes\/simula\u00e7\u00f5es Num\u00e9ricas<\/a> (Prof. Per-Olof Persson, UC Berkeley Mathematics)<\/li><\/ol>\n\n\n\n<h1 class=\"wp-block-heading\">Material de Apoio Did\u00e1tico<\/h1>\n\n\n\n<h1 class=\"wp-block-heading\">Refer\u00eancias Bibliogr\u00e1ficas:<\/h1>\n\n\n\n<ul class=\"wp-block-list\"><li>R. L, Burden e J. D. Faires. <em>An\u00e1lise Num\u00e9rica<\/em>. Cencage Learning, S\u00e3o Paulo,Janeiro, 2013.<\/li><li>Steven Chapra e Raymond P. Canale. <a href=\"https:\/\/www.amazon.com.br\/M%C3%A9todos-Num%C3%A9ricos-Engenharia-Steven-Chapra\/dp\/8586804878\">M\u00e9todos num\u00e9ricos para engenharia<\/a>. McGraw-Hill &#8211; S\u00e3o Paulo, 5a edi\u00e7\u00e3o, 2011.<\/li><li>Mauro A. Rincon e I-Shih Liu. <a href=\"https:\/\/dcc.ufrj.br\/~rincon\/#book\">Introdu\u00e7\u00e3o ao M\u00e9todo de Elementos Finitos &#8211; An\u00e1lise e Aplica\u00e7\u00f5es<\/a>. Instituto de Matem\u00e1tica, UFRJ, 2015. (c\u00f3pia <a href=\"https:\/\/dcc.ufrj.br\/~rincon\/MEF2016.pdf\">PDF<\/a>)<\/li><li>Jos\u00e9 A. Cuminato, Messias M. Junior. <a href=\"https:\/\/loja.sbm.org.br\/index.php\/sbm\/colecao-matematica-aplicada\/discretizac-o-de-equacoes-diferenciais-parciais.html\">Discretiza\u00e7\u00e3o de Equa\u00e7\u00f5es Diferenciais Parciais<\/a>. SBM, 2013.<\/li><li>Jonathan Whiteley. <a href=\"https:\/\/www.amazon.com.br\/Finite-Element-Methods-Practical-Guide\/dp\/3319842889\">Finite Element Methods: A Practical Guide<\/a>. Springer, 2017.<\/li><li>Larson, M. G. and Bengzon, F. <a rel=\"noreferrer noopener\" href=\"http:\/\/www.springer.com\/la\/book\/9783642332869\" target=\"_blank\"><em>The Finite Element Method: Theory, Implementation, and Applications<\/em><\/a>. Springer, 2013<\/li><li>Mark S. Gockenbach.&nbsp;<a rel=\"noreferrer noopener\" href=\"http:\/\/bookstore.siam.org\/ot97\/\" target=\"_blank\"><em>Understanding and implementing the finite element method<\/em><\/a>.&nbsp;Society for Industrial and Applied Mathematics (SIAM), 2006.<\/li><li>J.&nbsp;T.&nbsp;Oden,&nbsp;E.&nbsp;B.&nbsp;Becker,&nbsp;G.&nbsp;F.&nbsp;Carey. <a rel=\"noreferrer noopener\" href=\"https:\/\/www.amazon.com\/Finite-Elements-Introduction-Tinsley-Oden\/dp\/0133170578\" target=\"_blank\"><em>Finite&nbsp;Elements:&nbsp;An&nbsp;Introduction<\/em><\/a>. Vol 1,&nbsp;Prentice\u00ad Hall,&nbsp;1981.<\/li><li>Jean Donea and Antonio Huerta. <em><a rel=\"noreferrer noopener\" href=\"http:\/\/www.wiley.com\/WileyCDA\/WileyTitle\/productCd-0471496669.html\" target=\"_blank\">Finite Element Methods for Flow Problems<\/a>.<\/em>&nbsp;John Wiley &amp; Sons, 2003.<\/li><li>Marcia A. G. Ruggiero e Vera L. R. Lopes. C\u00e1lculo num\u00e9rico: aspectos te\u00f3ricos e computacionais.&nbsp;Pearson Education do Brasil, S\u00e3o Paulo, 2a edi\u00e7\u00e3o, 2013.<\/li><li>Dongarra, J.J., Duff, I.S., Sorasen, D.C., Van der Vorst, H.A., Numerical Linear Algebra for High-Performance Computers, SIAM, 1998.<\/li><li>Lloyd N. Trefethen and D. Bau. <em><a href=\"http:\/\/people.maths.ox.ac.uk\/trefethen\/books.html\">Numerical Linear Algebra<\/a>.<\/em> SIAM (1999).<\/li><li>D. Kincaid and W. Cheney. <em><a href=\"https:\/\/www.amazon.com\/Numerical-Analysis-Mathematics-Scientific-Undergraduate\/dp\/0821847880\">Numerica Analysis: Mathematics of Scientific Computing<\/a><\/em>. 3<sup>rd<\/sup> Ed, Brooks\/Cole, (2002).<\/li><li>L. M. Carvalho, S. Gratton, R. Lago e N. Maculan. <em>\u00c1lgebra Linear Num\u00e9rica e Computacional: m\u00e9todos de Krylov para a solu\u00e7\u00e3o de sistemas lineares<\/em>. Editora Ci\u00eancia Moderna, 2010.<\/li><li>Golub, G. and Van Loan, C., &#8220;Matrix Computations&#8221;, The John Hopkins University Press,1993.<\/li><li>Kelley C.T., &#8220;<a href=\"https:\/\/archive.siam.org\/books\/textbooks\/fr16_book.pdf\">Iterative Methods for Linear and Nonlinear Equations<\/a>&#8220;, SIAM, 1995.<\/li><li>Saad, Y., &#8220;<a href=\"https:\/\/www-users.cs.umn.edu\/~saad\/IterMethBook_2ndEd.pdf\">Iterative Methods for Sparse Linear Systems<\/a>&#8220;, PWS Publishing Company, 1996.<\/li><li>D. Hanselman e B. Littlefield. <em>MATLAB 6 \u2014 Curso completo.<\/em> Pearson Education do Brasil, S\u00e3o Paulo, 2a edi\u00e7\u00e3o, 2003.<\/li><li>Cleve Moler. <em><a href=\"https:\/\/www.mathworks.com\/moler\/chapters.html\">Numerical Computing with MATLAB<\/a>, 2004.<\/em><\/li><\/ul>\n\n\n\n<p><\/p>\n","protected":false},"excerpt":{"rendered":"<p>Objetivo da disciplina: Estudar de forma introdut\u00f3ria os m\u00e9todos de diferen\u00e7as finitas e elementos finitos para solu\u00e7\u00e3o de modelos matem\u00e1ticos baseados em equa\u00e7\u00f5es diferenciais parciais Cursos: Matem\u00e1tica Industrial Hor\u00e1rio das aulas: quartas 09:00 &#8211; 11:00&nbsp; (Sala 11 &#8211; Eixo 1) &hellip; <a href=\"https:\/\/blog.ufes.br\/isaacsantos\/ensino\/metodos-numericos-ii-2020-1\/\">Continue lendo <span class=\"meta-nav\">&rarr;<\/span><\/a><\/p>\n","protected":false},"author":279,"featured_media":0,"parent":73,"menu_order":0,"comment_status":"closed","ping_status":"closed","template":"","meta":{"_bbp_topic_count":0,"_bbp_reply_count":0,"_bbp_total_topic_count":0,"_bbp_total_reply_count":0,"_bbp_voice_count":0,"_bbp_anonymous_reply_count":0,"_bbp_topic_count_hidden":0,"_bbp_reply_count_hidden":0,"_bbp_forum_subforum_count":0,"_uag_custom_page_level_css":"","footnotes":""},"class_list":["post-660","page","type-page","status-publish","hentry"],"uagb_featured_image_src":{"full":false,"thumbnail":false,"medium":false,"medium_large":false,"large":false,"1536x1536":false,"2048x2048":false,"post-thumbnail":false,"large-feature":false,"small-feature":false},"uagb_author_info":{"display_name":"Isaac","author_link":"https:\/\/blog.ufes.br\/isaacsantos\/author\/isaac_pinheiro-dos-santos\/"},"uagb_comment_info":0,"uagb_excerpt":"Objetivo da disciplina: Estudar de forma introdut\u00f3ria os m\u00e9todos de diferen\u00e7as finitas e elementos finitos para solu\u00e7\u00e3o de modelos matem\u00e1ticos baseados em equa\u00e7\u00f5es diferenciais parciais Cursos: Matem\u00e1tica Industrial Hor\u00e1rio das aulas: quartas 09:00 &#8211; 11:00&nbsp; (Sala 11 &#8211; Eixo 1) &hellip; Continue lendo &rarr;","_links":{"self":[{"href":"https:\/\/blog.ufes.br\/isaacsantos\/wp-json\/wp\/v2\/pages\/660","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/blog.ufes.br\/isaacsantos\/wp-json\/wp\/v2\/pages"}],"about":[{"href":"https:\/\/blog.ufes.br\/isaacsantos\/wp-json\/wp\/v2\/types\/page"}],"author":[{"embeddable":true,"href":"https:\/\/blog.ufes.br\/isaacsantos\/wp-json\/wp\/v2\/users\/279"}],"replies":[{"embeddable":true,"href":"https:\/\/blog.ufes.br\/isaacsantos\/wp-json\/wp\/v2\/comments?post=660"}],"version-history":[{"count":16,"href":"https:\/\/blog.ufes.br\/isaacsantos\/wp-json\/wp\/v2\/pages\/660\/revisions"}],"predecessor-version":[{"id":681,"href":"https:\/\/blog.ufes.br\/isaacsantos\/wp-json\/wp\/v2\/pages\/660\/revisions\/681"}],"up":[{"embeddable":true,"href":"https:\/\/blog.ufes.br\/isaacsantos\/wp-json\/wp\/v2\/pages\/73"}],"wp:attachment":[{"href":"https:\/\/blog.ufes.br\/isaacsantos\/wp-json\/wp\/v2\/media?parent=660"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}