Mercoledì 17 aprile 2024 alle ore 16:30, nel quadro della serie di seminari Insalate di Matematica, Manuel Trezzi (Università degli Studi di Pavia) parlerà di
Titolo: 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
Informazioni per partecipare in presenza
Il seminario si svolgerà nell'Aula 3014, presso l'Edificio U5-Ratio dell'Università degli Studi di Milano-Bicocca.
Informazioni per partecipare online
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