Wednesday 17 April 2024 at 4:30 pm, as part of the Insalate di Matematica seminar series, Manuel Trezzi (University of Pavia) will talk about
Title: The Lightning Virtual Element Method
Abstract: The Virtual Element Method (VEM) is a method for discretizing partial differential equations (PDEs)developed in 2013. This talk introduces the Lightning Virtual Element Method (LVEM). This new VEM eliminates thestabilization term by actually computing the basis functions using rational functions. Thanks to the lightning Laplacesolver by N. Trefethen, the LVEM approximates the basis functions using rational functions with poles clusteredexponentially close to the corners of each element of the polygonal tessellation. This results in two great advantages.First, the mathematical analysis of a priori error estimates is much easier and essentially identical to the one for anyother non-conforming Galerkin discretization. Second, the fact that the lightning VEM computes the basis functionsallows the user to access the point-wise value of the numerical solution without needing any reconstructiontechniques. The cost of the local construction of the VEM basis is the implementation price that one has to pay for theadvantages of the lightning VEM method, but the parallelizable nature of this operation will ultimately result in a cost-efficient scheme compared to standard VEM and FEM.
Keywords: Virtual Element Method, Rational Functions, Stabilization free
Information to attend in presence
The seminar will take place in Room 3014, in Building U5-Ratio of the University of Milano-Bicocca.
Information to attend online
Visit the page: https://unimib.webex.com/unimib/j.php?MTID=m101728a0c0258813b6aa97783fb11fad
(password: insalate, 46725283 from phones)