[vc_row][vc_column width=”2\/3″][vc_column_text]<\/p>\n
[divider style=”solid” padding_top=”15″ padding_bottom=”0″][\/divider]<\/p>\n
[divider style=”solid” padding_top=”0″ padding_bottom=”15″][\/divider]<\/p>\n
Computing the solutions $u$ of an equation $f(u, \\lambda) = 0$ as the parameter $\\lambda$ is varied is a central task in applied mathematics and engineering. In this talk I will present a new algorithm, deflated continuation, for this task.<\/p>\n
Deflated continuation has three main advantages. First, it is capable of computing disconnected bifurcation diagrams; previous algorithms only aimed to compute that part of the bifurcation diagram continuously connected to the initial data. Second, its implementation is extremely simple: it only requires a minor modification to any existing Newton-based solver. Third, it can scale to very large discretisations if a good preconditioner is available.<\/p>\n
Among other problems, we will apply this to a famous singularly perturbed ODE, Carrier’s problem. The computations reveal a striking and beautiful bifurcation diagram, with an infinite sequence of alternating pitchfork and fold bifurcations as the singular perturbation parameter tends to zero. The analysis yields a novel and complete taxonomy of the solutions to the problem, and demonstrates that a claim of Bender & Orszag (1999) is incorrect. We will also use the algorithm to calculate distinct local minimisers of a topology optimisation problem via the combination of deflated continuation and a semismooth Newton method.[\/vc_column_text][vc_empty_space height=”35px”][vc_toggle title=”Personal bio of Prof Patrick Farrell” style=”square” el_id=”1472579256290-0895b46c-c616″]<\/p>\n
Employment:<\/strong> Associate Professor in Numerical Analysis and Scientific Computing Mathematical Institute , University of Oxford and Tutorial Fellow in Applied Mathematics – Oriel College, University of Oxford<\/p>\n Qualifications:<\/strong> PhD in Computational Physics – Imperial College London – Thesis title:<\/strong> Galerkin projection of discrete fields via supermesh construction<\/p>\n Prizes:<\/strong> Association of Computational Mechanics in Engineering 2010; Finalist and UK Representative, European Community on Computational Methods in Applied Sciences Award; Fox Prize, 2015, Wilkinson Prize 2015<\/p>\n [\/vc_toggle][vc_empty_space height=”10px”][\/vc_column][vc_column width=”1\/3″ css=”.vc_custom_1458822913427{margin-left: 15px !important;padding-top: 15px !important;padding-right: 15px !important;padding-bottom: 15px !important;padding-left: 15px !important;background-color: #f1f1f2 !important;}”][vc_custom_heading text=”Details” font_container=”tag:h2|font_size:20|text_align:left” google_fonts=”font_family:Raleway%3A100%2C200%2C300%2Cregular%2C500%2C600%2C700%2C800%2C900|font_style:700%20bold%20regular%3A700%3Anormal”][vc_column_text]Date:<\/strong>\u00a019\u00a0APRIL 2017 Address<\/strong> Phone: <\/strong>+55 11 2648-6226[\/vc_column_text][vc_separator color=”#424242″ padding_top=”12″ padding_bottom=”12″][vc_raw_html]JTNDZGl2JTIwY2xhc3MlM0QlMjJmYi1zaGFyZS1idXR0b24lMjIlMjBkYXRhLWhyZWYlM0QlMjJodHRwJTNBJTJGJTJGd3d3LnJjZ2kucG9saS51c3AuYnIlMkZldmVudHMtMjAxNiUyRjEyOS1iaWZ1cmNhdGlvbnMtYnVja2xpbmctYW5kLWZsb3ctdHJhbnNpdGlvbnMlMkYlMjIlMjBkYXRhLWxheW91dCUzRCUyMmJ1dHRvbiUyMiUzRSUzQyUyRmRpdiUzRQ==[\/vc_raw_html][vc_empty_space height=”20px”][vc_tweetmeme][vc_separator color=”#424242″ padding_top=”12″ padding_bottom=”12″][vc_button title=”Download the event poster” target=”_blank” icon_fontawesome=”fa fa-angle-down” align=”left” add_icon=”true” href=”\/wp-content\/uploads\/2017\/04\/poster_19.04.2017.pdf”][\/vc_column][\/vc_row]<\/p>\n","protected":false},"excerpt":{"rendered":" [vc_row][vc_column width=”2\/3″][vc_column_text] 19\u00a0APRIL 2017 | SEMINAR\u00a0 BIFURCATIONS, BUCKLING AND FLOW TRANSITIONS Scalable bifurcation analysis of nonlinear partial differential equations and variational inequalities [divider style=”solid” padding_top=”15″ padding_bottom=”0″][\/divider] Prof Patrick Farrell Mathematical … <\/p>\n
\nTime:<\/strong> 2:00 pm<\/p>\n
\nRCGI – Research Centre for Gas Innovation
\nPr\u00e9dio da Engenharia Mec\u00e2nica e Naval
\nAv. Professor Mello Moraes, 2231
\nUniversity of S\u00e3o Paulo
\nEscola Polit\u00e9cnica | Cidade Universit\u00e1ria
\nS\u00e3o Paulo – SP, 05508-030 | Brazil<\/p>\n