English
Related papers

Related papers: Virtual Element based formulations for computation…

200 papers

We study, both theoretically and numerically, the equilibrium of a hinged rigid leaflet with an attached rotational spring, immersed in a stationary incompressible fluid within a rigid channel. Through a careful investigation of the…

Numerical Analysis · Mathematics 2020-07-20 L. Beirão da Veiga , C. Canuto , R. H. Nochetto , G. Vacca

The Virtual Element Method (VEM) is a Galerkin approximation method that extends the Finite Element Method (FEM) to polytopal meshes. In this paper, we present a conforming formulation that generalizes the Scott-Vogelius finite element…

Numerical Analysis · Mathematics 2021-12-28 Gianmarco Manzini , Annamaria Mazzia

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…

Numerical Analysis · Mathematics 2015-05-20 Ilaria Perugia , Paola Pietra , Alessandro Russo

This paper presents an initial exploration of stress-assisted diffusion problems in three dimensions within the framework of the virtual element method (VEM). Hilbert spaces enriched with parameter-weighted norms, the extended…

Numerical Analysis · Mathematics 2025-02-05 Andres E. Rubiano

The Virtual Element Method (VEM) is a very effective framework to design numerical approximations with high global regularity to the solutions of elliptic partial differential equations. In this paper, we review the construction of such…

Numerical Analysis · Mathematics 2021-12-28 Paola Francesca Antonietti , Gianmarco Manzini , Simone Scacchi , Marco Verani

Concrete heterogeneity originates from its production process, which involves bonding aggregates with a binder matrix. This study presents a mesoscale finite element model (MFEM) that offers detailed insights into the fracture process at…

Materials Science · Physics 2025-09-17 Jan Mašek , Petr Miarka

The modeling of large deformation fracture mechanics has been a challenging problem regarding the accuracy of numerical methods and their ability to deal with considerable changes in deformations of meshes where having the presence of…

Numerical Analysis · Computer Science 2019-03-21 Hai D. Huynh , Phuong Tran , Xiaoying Zhuang , H. Nguyen-Xuan

We design a virtual element method for the numerical treatment of the two-dimensional parabolic variational inequality problem on unstructured polygonal meshes. Due to the expected low regularity of the exact solution, the virtual element…

Numerical Analysis · Mathematics 2021-06-01 Dibyendu Adak , Gianmarco Manzini , Sundararajan Natarajan

We present an optimization procedure for generic polygonal or polyhedral meshes, tailored for the Virtual Element Method (VEM). Once the local quality of the mesh elements is analyzed through a quality indicator specific to the VEM, groups…

Numerical Analysis · Mathematics 2024-11-08 Tommaso Sorgente , Stefano Berrone , Silvia Biasotti , Gianmarco Manzini , Michela Spagnuolo , Fabio Vicini

In this paper we consider a coupled bulk-surface PDE in two space dimensions. The model consists of a PDE in the bulk that is coupled to another PDE on the surface through general nonlinear boundary conditions. For such a system we propose…

Numerical Analysis · Mathematics 2022-11-07 Massimo Frittelli , Anotida Madzvamuse , Ivonne Sgura

A three-dimensional multi-scale computational homogenisation framework is developed for the prediction of nonlinear micro/meso-mechanical response of the fibre-reinforced polymer (FRP) composites. Two dominant damage mechanisms, i.e. matrix…

Computational Engineering, Finance, and Science · Computer Science 2016-10-18 Zahur Ullah , Lukasz Kaczmarczyk , Chris J. Pearce

In this work we present a novel bulk-surface virtual element method (BSVEM) for the numerical approximation of elliptic bulk-surface partial differential equations (BSPDEs) in three space dimensions. The BSVEM is based on the discretisation…

Numerical Analysis · Mathematics 2023-05-24 Massimo Frittelli , Anotida Madzvamuse , Ivonne Sgura

A new field of numerical astrophysics is introduced which addresses the solution of large, multidimensional structural or slowly-evolving problems (rotating stars, interacting binaries, thick advective accretion disks, four dimensional…

Astrophysics · Physics 2009-10-30 David L. Meier

In this article we propose and numerically implement a mathematical model for the simulation of three-dimensional semiconductor devices characterized by an heterogeneous material structure. The model consists of a system of nonlinearly…

Numerical Analysis · Mathematics 2013-07-12 A. Mauri , R. Sacco , M. Verri

In this paper, we employ the linear virtual element spaces to discretize the semilinear sine-Gordon equation in two dimensions. The salient features of the virtual element method (VEM) are: (a) it does not require explicit form of the shape…

Numerical Analysis · Mathematics 2019-12-12 Dibyendu Adak , Sundararajan Natarajan

We propose a computational framework, Hetero-EUCLID, for segmentation and parameter identification to characterize the full hyperelastic behavior of all constituents of a heterogeneous material. In this work, we leverage the Bayesian-EUCLID…

Computational Engineering, Finance, and Science · Computer Science 2026-01-19 Kanhaiya Lal Chaurasiya , Saurav Dutta , Siddhant Kumar , Akshay Joshi

We present the non-conforming Virtual Element Method (VEM) for the numerical approximation of velocity and pressure in the steady Stokes problem. The pressure is approximated using discontinuous piecewise polynomials, while each component…

Numerical Analysis · Mathematics 2016-09-07 Andrea Cangiani , Vitaliy Gyrya , Gianmarco Manzini

Flexible piezoelectric devices made of polymeric materials are widely used for micro- and nano-electro-mechanical systems. In particular, numerous recent applications concern energy harvesting. Due to the importance of computational…

Computational Engineering, Finance, and Science · Computer Science 2015-07-28 Claudio Maruccio , Laura De Lorenzis , Luana Persano , Dario Pisignano

Real-world physical systems, like composite materials and porous media, exhibit complex heterogeneities and multiscale nature, posing significant computational challenges. Computational homogenization is useful for predicting macroscopic…

Computational Engineering, Finance, and Science · Computer Science 2024-07-29 Yuki Sato , Yuto Lewis Terashima , Ruho Kondo

We introduce a novel virtual element method (VEM) for the two dimensional Helmholtz problem endowed with impedance boundary conditions. Local approximation spaces consist of Trefftz functions, i.e., functions belonging to the kernel of the…

Numerical Analysis · Mathematics 2018-10-26 L. Mascotto , I. Perugia , A. Pichler