A Plane Wave Virtual Element Method for the Helmholtz Problem
By Ilaria Perugia, Paola Pietra, Alessandro Russo. 2015
145 citations recorded by the source corpus.
We introduce and analyze a virtual element method (VEM) for the Helmholtz problem with approximating spaces made of products of low order VEM functions and plane waves. We restrict ourselves to the 2D Helmholtz equation with impedance boundary conditions on the whole domain boundary. The main ingredients of the plane wave VEM scheme are: i) a low frequency space made of VEM functions, whose basis functions are not explicitly computed in the element interiors; ii) a proper local projection operator onto the high-frequency space, made of plane waves; iii) an approximate stabilization term. A convergence result for the h-version of the method is proved, and numerical results testing its performance on general polygonal meshes are presented.
Subfields: Computational Mechanics, Electrical and Electronic Engineering, Mechanics of Materials
View Paper: https://www.semanticscholar.org/paper/662ea8f3adba70b03c7b4126527fa25b5414e69f
How researchers see this paper
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In Computational Mechanics
- Paola Francesca Antonietti
- Gianmarco Manzini
- Marco Verani
- Lorenzo Mascotto
- Elena Benvenuti
- Natarajan Sukumar
- Andrea Chiozzi
- David Mora
In Electrical and Electronic Engineering
- Gianmarco Manzini
- Elena Benvenuti
- Andrea Chiozzi
- Paola Francesca Antonietti
- Lorenzo Mascotto
- Marco Verani
- Natarajan Sukumar
- David Mora
In Mechanics of Materials
- Gianmarco Manzini
- Paola Francesca Antonietti
- Marco Verani
- Lorenzo Mascotto
- Elena Benvenuti
- Andrea Chiozzi
- Natarajan Sukumar
- David Mora
Citations in the corpus
- A multigrid algorithm for the $p$-version of the Virtual Element Method (2017, background): “VEMs for linear and nonlinear elasticity have been developed in [18, 21, 50], whereas VEMs for plate bending, Cahn-Hilliard, Stokes, and Helmholtz problems have been addressed in [6, 8, 34, 55].”
- Extended virtual element method for the Laplace problem with singularities and discontinuities (2019, background): “[11] were the first to introduce approximating spaces that”
- Virtual element for the buckling problem of Kirchhoff–Love plates (2019, background): “in a large range of problems in fluid and solid mechanics; see for instance [2, 3, 4, 7, 8, 9, 11, 12, 15, 16, 21, 22, 23, 24, 33, 40, 43, 44].”