<div dir="ltr"><p style="font-variant-numeric:normal;font-variant-east-asian:normal;font-stretch:normal;font-size:14px;line-height:normal;font-family:Helvetica;margin:0px;color:rgb(0,0,0)">Nell&#39;ambito del progetto <i>Se mi narri di Matematica</i>,</p><p style="font-variant-numeric:normal;font-variant-east-asian:normal;font-stretch:normal;font-size:14px;line-height:normal;font-family:Helvetica;margin:0px;color:rgb(0,0,0)"><br></p><p style="font-variant-numeric:normal;font-variant-east-asian:normal;font-stretch:normal;font-size:14px;line-height:normal;font-family:Helvetica;margin:0px;color:rgb(0,0,0)">Data e ora: <b>10 dicembre 2020, ore 16:15 </b></p><p style="font-variant-numeric:normal;font-variant-east-asian:normal;font-stretch:normal;font-size:14px;line-height:normal;font-family:Helvetica;margin:0px;color:rgb(0,0,0)">Speaker: <span style="white-space:pre-wrap">        </span>Monica Montardini (Università degli Studi di Pavia) </p><p style="font-variant-numeric:normal;font-variant-east-asian:normal;font-stretch:normal;font-size:14px;line-height:normal;font-family:Helvetica;margin:0px;color:rgb(0,0,0)">Titolo: <span style="white-space:pre-wrap">        </span><i>A space-time Galerkin isogeometric method and related efficient solver for the heat equation</i></p><p style="font-variant-numeric:normal;font-variant-east-asian:normal;font-stretch:normal;font-size:14px;line-height:normal;font-family:Helvetica;margin:0px;color:rgb(0,0,0)">Abstract: </p><p style="font-variant-numeric:normal;font-variant-east-asian:normal;font-stretch:normal;font-size:14px;line-height:normal;font-family:Helvetica;margin:0px;color:rgb(0,0,0)">Isogeometric Analysis (IgA) is an evolution of the finite element method: it employs B-splines or their generalization both to represent the computational domain and to approximate the solution of the considered partial differential equation. The high-continuity of isogeometric basis functions leads to several advantages, e.g. higher accuracy per degree-of-freedom, but it introduces challenging problems at the computational level: one of the major issues is the efficient solution of linear systems. The development of computationally efficient and robust preconditioners is a challenge in IgA community. Indeed, a good preconditioner helps the convergence of iterative methods, that in IgA are preferred to the direct ones.</p><p style="font-variant-numeric:normal;font-variant-east-asian:normal;font-stretch:normal;font-size:14px;line-height:normal;font-family:Helvetica;margin:0px;color:rgb(0,0,0);min-height:17px"><br></p><p style="font-variant-numeric:normal;font-variant-east-asian:normal;font-stretch:normal;font-size:14px;line-height:normal;font-family:Helvetica;margin:0px;color:rgb(0,0,0)">In this talk, after a brief introduction to IgA, I will focus on the study of an efficient solver for a Galerkin space-time isogeometric discretization of the heat equation. Exploiting the tensor product structure of the basis functions in the parametric domain, I propose a preconditioner that can be efficiently applied thanks to an extension of the classical Fast Diagonalization method. The preconditioner is robust with respect to the polynomial degree and the time required for the application is almost proportional to the number of degrees-of-freedom.  </p><p style="font-variant-numeric:normal;font-variant-east-asian:normal;font-stretch:normal;font-size:14px;line-height:normal;font-family:Helvetica;margin:0px;color:rgb(0,0,0);min-height:17px"><br></p><p style="font-variant-numeric:normal;font-variant-east-asian:normal;font-stretch:normal;font-size:14px;line-height:normal;font-family:Helvetica;margin:0px;color:rgb(0,0,0)">Dove:</p><p style="font-variant-numeric:normal;font-variant-east-asian:normal;font-stretch:normal;font-size:14px;line-height:normal;font-family:Helvetica;margin:0px;color:rgb(0,0,0)"><b>Aula Beltrami</b>, Dipartimento di Matematica.</p><p style="font-variant-numeric:normal;font-variant-east-asian:normal;font-stretch:normal;font-size:14px;line-height:normal;font-family:Helvetica;margin:0px;color:rgb(0,0,0);min-height:17px"><br></p><p style="font-variant-numeric:normal;font-variant-east-asian:normal;font-stretch:normal;font-size:14px;line-height:normal;font-family:Helvetica;margin:0px;color:rgb(0,0,0)">oppure</p><p style="font-variant-numeric:normal;font-variant-east-asian:normal;font-stretch:normal;font-size:14px;line-height:normal;font-family:Helvetica;margin:0px;color:rgb(0,0,0);min-height:17px"><br></p><p style="font-variant-numeric:normal;font-variant-east-asian:normal;font-stretch:normal;font-size:14px;line-height:normal;font-family:Helvetica;margin:0px;color:rgb(0,0,0)">Link Zoom: <a href="https://us02web.zoom.us/j/84296872461" target="_blank">https://us02web.zoom.us/j/84296872461</a></p><p style="font-variant-numeric:normal;font-variant-east-asian:normal;font-stretch:normal;font-size:14px;line-height:normal;font-family:Helvetica;margin:0px;color:rgb(0,0,0)"><b>Meeting ID: 842 9687 2461</b></p><p style="font-variant-numeric:normal;font-variant-east-asian:normal;font-stretch:normal;font-size:14px;line-height:normal;font-family:Helvetica;margin:0px;color:rgb(0,0,0)"><b>Passcode: 168170</b></p><p style="font-variant-numeric:normal;font-variant-east-asian:normal;font-stretch:normal;font-size:14px;line-height:normal;font-family:Helvetica;margin:0px;color:rgb(0,0,0);min-height:17px"><br></p><p style="font-variant-numeric:normal;font-variant-east-asian:normal;font-stretch:normal;font-size:14px;line-height:normal;font-family:Helvetica;margin:0px;color:rgb(0,0,0)"><span style="text-decoration-line:underline">Informazioni importanti riguardo allo svolgimento dei seminari:</span></p><ul><li style="margin:0px;font-variant-numeric:normal;font-variant-east-asian:normal;font-stretch:normal;font-size:14px;line-height:normal;font-family:Helvetica;color:rgb(0,0,0)"><span style="font-variant-numeric:normal;font-variant-east-asian:normal;font-stretch:normal;font-size:16.8px;line-height:normal"></span><b>per coloro che intendono presenziare al seminario di persona, </b>si avvisa che, per le attuali disposizioni, l&#39;accesso è consentito a un numero massimo di 40 persone. Non è necessario passare dal punto di misurazione della temperatura, ma<b> verrà chiesto di segnalare il proprio nominativo su apposito registro, che verrà conservato per i 14 giorni successivi</b>;</li><li style="margin:0px;font-variant-numeric:normal;font-variant-east-asian:normal;font-stretch:normal;font-size:14px;line-height:normal;font-family:Helvetica;color:rgb(0,0,0)"><span style="font-variant-numeric:normal;font-variant-east-asian:normal;font-stretch:normal;font-size:16.8px;line-height:normal"></span>a causa delle misure di sicurezza della piattaforma Zoom, <b>è necessario inserire il passcode</b> per poter partecipare alla sessione;</li><li style="margin:0px;font-variant-numeric:normal;font-variant-east-asian:normal;font-stretch:normal;font-size:14px;line-height:normal;font-family:Helvetica;color:rgb(0,0,0)"><span style="font-variant-numeric:normal;font-variant-east-asian:normal;font-stretch:normal;font-size:16.8px;line-height:normal"></span>nel caso in cui il meeting si interrompesse per problemi di natura tecnica, seguiranno istruzioni pubblicate sia sul sito (<a href="http://matematica.unipv.it/seminaridott/index.html" target="_blank">http://matematica.unipv.it/seminaridott/</a>), sia sulla pagina facebook (<a href="https://www.facebook.com/seminarri/" target="_blank">https://www.facebook.com/seminarri/</a>);</li><li style="margin:0px;font-variant-numeric:normal;font-variant-east-asian:normal;font-stretch:normal;font-size:14px;line-height:normal;font-family:Helvetica;color:rgb(0,0,0)"><span style="font-variant-numeric:normal;font-variant-east-asian:normal;font-stretch:normal;font-size:16.8px;line-height:normal"></span>il seminario verrà registrato e il video verrà caricato sul sito. Partecipando all&#39;evento si dà il consenso ad essere registrati.</li></ul><p style="font-variant-numeric:normal;font-variant-east-asian:normal;font-stretch:normal;font-size:14px;line-height:normal;font-family:Helvetica;margin:0px;color:rgb(0,0,0)">Tutte le informazioni e gli aggiornamenti si trovano anche sulla pagina web (<a href="http://matematica.unipv.it/seminaridott/index.html" target="_blank">http://matematica.unipv.it/seminaridott/</a>) e su quella facebook (<a href="https://www.facebook.com/seminarri/" target="_blank">https://www.facebook.com/seminarri/</a>).</p><p style="font-variant-numeric:normal;font-variant-east-asian:normal;font-stretch:normal;font-size:14px;line-height:normal;font-family:Helvetica;margin:0px;color:rgb(0,0,0)">L&#39;invito si estende a tutti gli interessati.</p><p style="font-variant-numeric:normal;font-variant-east-asian:normal;font-stretch:normal;font-size:14px;line-height:normal;font-family:Helvetica;margin:0px;color:rgb(0,0,0);min-height:17px"><br></p><p style="font-variant-numeric:normal;font-variant-east-asian:normal;font-stretch:normal;font-size:14px;line-height:normal;font-family:Helvetica;margin:0px;color:rgb(0,0,0)"><span style="white-space:pre-wrap">        </span>gli organizzatori</p><p style="font-variant-numeric:normal;font-variant-east-asian:normal;font-stretch:normal;font-size:14px;line-height:normal;font-family:Helvetica;margin:0px;color:rgb(0,0,0)"><span style="white-space:pre-wrap">        </span>Mai, Silvia, Federico e Stefano</p></div>