Gianmarco Manzini, Los Alamos National Laboratory
Monday, December 3, 2018 -
3:30pm to 4:30pm
TITLE: The Virtual Element Method
We present the Virtual Element Method (VEM) for the numerical treatment of elliptic problems. The VEM is a disruptive innovation in the field of finite elements because the numerical approximation of problems in variational form is built as a finite element method but without the explicit knowledge of the basis functions. All integrals of the discrete variational formulations are computed directly from the degrees of freedom of the method through some special polynomial projection operators. This feature allows the VEM to be very flexible and work on very general unstructured meshes of polygons in 2D and polyhedra in 3D, with any order of accuracy and any order of regularity. We will present the conforming and nonconforming formulations and results from numerical experiments to verify the theory and validate the performance.
Dr. G. Manzini is an applied mathematician working on the development, analysis and implementation of numerical methods for partial differential equations. After his doctoral studies at CERFACS and Universite` "P. Sabatier" in Toulouse, France (1989-1994), he worked as a post-doc at CRS4 (1993-1996), Cagliari, Italy, in the group of Computational Mechanics led by Prof. A. Quarteroni. In 1997, he joined the "Istituto di Matematica Applicata e Tecnologie Informatiche" (IMATI) of the Consiglio Nazionale delle Ricerche (CNR) in Pavia, Italy, directed by Prof. F. Brezzi. In IMATI he currently holds a position of Research Director. In 2012, he joined the Applied Mathematics and Plasma Physics Group at the Los Alamos National Laboratory as a senior scientist, where he has been the principal investigator (PI) and co-PI of three research projects.