{"id":857,"date":"2019-11-20T14:11:08","date_gmt":"2019-11-20T14:11:08","guid":{"rendered":"https:\/\/iheart.polimi.it\/en\/?p=857"},"modified":"2025-02-21T08:51:25","modified_gmt":"2025-02-21T08:51:25","slug":"numerical-approximation-of-parametrized-problems-in-cardiac-electrophysiology-by-a-local-reduced-basis-method","status":"publish","type":"post","link":"https:\/\/iheart.polimi.it\/en\/it\/numerical-approximation-of-parametrized-problems-in-cardiac-electrophysiology-by-a-local-reduced-basis-method\/","title":{"rendered":"Numerical approximation of parametrized problems in cardiac electrophysiology by a local reduced basis method"},"content":{"rendered":"\n<p><em>Stefano Pagani, Andrea Manzoni, Alfio Quarteroni<\/em><\/p>\n\n\n\n<p><strong>Computer Methods in Applied Mechanics and Engineering<\/strong> Volume 340, 1 October 2018, Pages 530-558<\/p>\n\n\n\n<p>Open Access: <a href=\"https:\/\/www.sciencedirect.com\/science\/article\/pii\/S0045782518303001\" target=\"_blank\" rel=\"noreferrer noopener\">https:\/\/www.sciencedirect.com\/science\/article\/pii\/S0045782518303001<\/a><br>DOI: <a href=\"https:\/\/doi.org\/10.1016\/j.cma.2018.06.003\" target=\"_blank\" rel=\"noreferrer noopener\">https:\/\/doi.org\/10.1016\/j.cma.2018.06.003<\/a><\/p>\n\n\n\n<p><strong>Abstract:<\/strong><\/p>\n\n\n\n<p>The efficient solution of coupled PDEs\/ODEs problems arising in cardiac electrophysiology is of key importance whenever interested to study the electrical behavior of the tissue for several instances of relevant physical and\/or geometrical parameters. This poses significant challenges to reduced order modeling (ROM) techniques \u2013such as the reduced basis method \u2013traditionally employed when dealing with the repeated solution of parameter dependent differential equations. Indeed, the nonlinear nature of the problem, the presence of moving fronts in the solution, and the high sensitivity of this latter to parameter variations, make<br>the application of standard ROM techniques very problematic. In this paper we propose a local ROM built through a k-means clustering in the state space of the snapshots for both the solution and the nonlinear term. Several comparisons among alternative local ROMs on a benchmark test case show the effectivity of the proposed approach. Finally, the application to a parametrized problem set on an idealized left-ventricle geometry shows the capability of the proposed ROM to face complex problems.<\/p>\n","protected":false},"excerpt":{"rendered":"<p>Stefano Pagani, Andrea Manzoni, Alfio Quarteroni Computer Methods in Applied Mechanics and Engineering Volume 340, 1 October 2018, Pages 530-558 Open Access: https:\/\/www.sciencedirect.com\/science\/article\/pii\/S0045782518303001DOI: https:\/\/doi.org\/10.1016\/j.cma.2018.06.003 Abstract: The efficient solution of coupled PDEs\/ODEs problems arising in cardiac electrophysiology is of key importance whenever interested to study the electrical behavior of the tissue [&hellip;]<\/p>\n","protected":false},"author":2,"featured_media":509,"comment_status":"closed","ping_status":"closed","sticky":false,"template":"","format":"standard","meta":{"footnotes":""},"categories":[163,155,1],"tags":[],"class_list":["post-857","post","type-post","status-publish","format-standard","has-post-thumbnail","hentry","category-articoli","category-in-evidenza","category-uncategorized"],"_links":{"self":[{"href":"https:\/\/iheart.polimi.it\/en\/wp-json\/wp\/v2\/posts\/857","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/iheart.polimi.it\/en\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/iheart.polimi.it\/en\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/iheart.polimi.it\/en\/wp-json\/wp\/v2\/users\/2"}],"replies":[{"embeddable":true,"href":"https:\/\/iheart.polimi.it\/en\/wp-json\/wp\/v2\/comments?post=857"}],"version-history":[{"count":1,"href":"https:\/\/iheart.polimi.it\/en\/wp-json\/wp\/v2\/posts\/857\/revisions"}],"predecessor-version":[{"id":858,"href":"https:\/\/iheart.polimi.it\/en\/wp-json\/wp\/v2\/posts\/857\/revisions\/858"}],"wp:featuredmedia":[{"embeddable":true,"href":"https:\/\/iheart.polimi.it\/en\/wp-json\/wp\/v2\/media\/509"}],"wp:attachment":[{"href":"https:\/\/iheart.polimi.it\/en\/wp-json\/wp\/v2\/media?parent=857"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/iheart.polimi.it\/en\/wp-json\/wp\/v2\/categories?post=857"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/iheart.polimi.it\/en\/wp-json\/wp\/v2\/tags?post=857"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}