A Plane Wave Virtual Element Method for the Helmholtz Problem

Prof. Ilaria Perugia, University of Vienna

6 Jul 2015, 17:00–18:30; Location: S4|10-1

The Virtual Element Method (VEM) is a generalisation of the finite element method recently introduced by Beirao da Veiga, Brezzi, Cangiani, Manzini, Marini and Russo in 2013, which takes inspiration from modern mimetic finite difference schemes, and allows to use very general polygonal/polyhedral meshes. 

This talk is concerned with a new method based on inserting plane wave basis functions within the VEM framework in order to construct a conforming, high-order method for the discretisation of the Helmholtz problem. The main ingredients of this plane wave VEM (PW-VEM) are: i) a low frequency space, whose basis functions are not explicitly computed in the element interiors; ii) a proper local projection operator onto a high-frequency space, which has to provide good approximation properties for Helmholtz solutions, and to allow to compute exactly the bilinear form, whenever one of the two entries belongs to that space; iii) an approximate stabilisation term.
The PW-VEM will be derived, and an outline of its convergence analysis will be presented, as well as some numerical testing.

These results have been obtained in collaboration with Paola Pietra (IMATI-CNR "E. Magenes'', Pavia, Italy) and Alessandro Russo (Università di Milano Bicocca, Milano, Italy).

Category: CE Seminar


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