4.7 Article

A virtual element method for the solution of 2D time-harmonic elastic wave equations via scalar potentials

相关参考文献

注意:仅列出部分参考文献,下载原文获取全部文献信息。
Article Mathematics, Applied

CVEM-BEM Coupling for the Simulation of Time-Domain Wave Fields Scattered by Obstacles with Complex Geometries

Luca Desiderio et al.

Summary: In this paper, a numerical method combining Curved Virtual Element Method (CVEM) and Boundary Element Method (BEM) is proposed for simulating wave field scattering by obstacles in homogeneous infinite media. The method considers the 2D time-domain damped wave equation with a Dirichlet condition on the boundary (sound-soft scattering). To handle the infinite domain, an artificial boundary is introduced with a Non-Reflecting Boundary Condition (BI-NRBC). CVEM with Crank-Nicolson time integrator is used in the interior domain, and BI-NRBC is discretized using a convolution quadrature formula in time and a collocation method in space. Numerical results demonstrate the effectiveness of the proposed approach, especially for obstacles with complex geometries.

COMPUTATIONAL METHODS IN APPLIED MATHEMATICS (2023)

Article Mathematics, Applied

Two FEM-BEM methods for the numerical solution of 2D transient elastodynamics problems in unbounded domains

S. Falletta et al.

Summary: We consider wave propagation problems in 2D unbounded isotropic homogeneous elastic media with rigid boundary conditions. Two alternative numerical approaches are proposed and compared, both obtained by coupling the differential equation with the associated space-time boundary integral equation. The integral equation defines a non-reflecting boundary condition for incoming and outgoing waves. The construction and implementation of these approaches are described and discussed, and numerical tests are conducted.

COMPUTERS & MATHEMATICS WITH APPLICATIONS (2022)

Article Mathematics, Applied

CVEM-BEM Coupling with Decoupled Orders for 2D Exterior Poisson Problems

Luca Desiderio et al.

Summary: In this study, a coupling method combining the Curved Virtual Element Method (CVEM) and the Boundary Element Method (BEM) is proposed to solve 2D exterior Dirichlet Poisson problems. The decoupled approximation orders allow for separating the contributions of CVEM and BEM to the error, achieving an accurate discrete solution by utilizing the high order flexibility of CVEM with a low order BEM. Numerical results validate the a priori estimates and demonstrate the effectiveness of the proposed approach.

JOURNAL OF SCIENTIFIC COMPUTING (2022)

Article Mathematics, Applied

ON THE COUPLING OF THE CURVED VIRTUAL ELEMENT METHOD WITH THE ONE-EQUATION BOUNDARY ELEMENT METHOD FOR 2D EXTERIOR HELMHOLTZ PROBLEMS\ast

Luca Desiderio et al.

Summary: In this paper, we discuss the solution of the Helmholtz equation with a nonconstant coefficient in unbounded domains. We propose a method that reduces the infinite domain to a bounded computational domain and combines the virtual element method and the boundary element method to solve the problem. Theoretical analysis and numerical tests show the effectiveness of this approach.

SIAM JOURNAL ON NUMERICAL ANALYSIS (2022)

Article Engineering, Multidisciplinary

The arbitrary-order virtual element method for linear elastodynamics models: convergence, stability and dispersion-dissipation analysis

Paola F. Antonietti et al.

Summary: The study introduces the conforming virtual element method for numerical approximation of two-dimensional elastodynamics problem, proves stability and convergence of the method, and derives optimal error estimates under different refinements. Experimental results demonstrate the method's effectiveness on various computational meshes and show exponential convergence under p-refinement. Dispersion-dissipation analysis reveals that polygonal meshes exhibit similar properties to classical simplicial/quadrilateral grids.

INTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN ENGINEERING (2021)

Article Mathematics, Applied

NUMERICAL ANALYSIS OF A METHOD FOR SOLVING 2D LINEAR ISOTROPIC ELASTODYNAMICS WITH TRACTION FREE BOUNDARY CONDITION USING POTENTIALS AND FINITE ELEMENTS

Jorge Albella Martinez et al.

Summary: This study decouples the elastodynamic equations using a Helmholtz decomposition and reviews the challenges of stability when dealing with traction-free boundary conditions, proposing a solution and providing a complete stability analysis of the numerical scheme.

MATHEMATICS OF COMPUTATION (2021)

Article Mathematics, Applied

A Virtual Element Method coupled with a Boundary Integral Non Reflecting condition for 2D exterior Helmholtz problems

L. Desiderio et al.

Summary: A new numerical approach is presented for solving 2D exterior Helmholtz problems in unbounded domains by reducing the infinite region to a finite computational domain Omega with the introduction of an artificial boundary B and applying a Virtual Element Method (VEM) within Omega. The method achieves optimal convergence order by choosing the same approximation order for VEM and BI-NRBC discretization spaces, and its efficiency and accuracy are demonstrated through various numerical examples from literature and real life applications.

COMPUTERS & MATHEMATICS WITH APPLICATIONS (2021)

Article Mathematics, Applied

THE VIRTUAL ELEMENT METHOD WITH CURVED EDGES

L. Beirao da Veiga et al.

ESAIM-MATHEMATICAL MODELLING AND NUMERICAL ANALYSIS-MODELISATION MATHEMATIQUE ET ANALYSE NUMERIQUE (2019)

Article Mathematics, Applied

Two boundary integral equation methods for linear elastodynamics problems on unbounded domains

S. Falletta et al.

COMPUTERS & MATHEMATICS WITH APPLICATIONS (2019)

Article Mathematics, Applied

Solving 2D Linear Isotropic Elastodynamics by Means of Scalar Potentials: A New Challenge for Finite Elements

Jorge Albella Martinez et al.

JOURNAL OF SCIENTIFIC COMPUTING (2018)

Article Mathematics, Applied

Stability analysis for the virtual element method

Lourenco Beirao da Veiga et al.

MATHEMATICAL MODELS & METHODS IN APPLIED SCIENCES (2017)

Article Mathematics, Applied

A posteriori error estimates for the virtual element method

Andrea Cangiani et al.

NUMERISCHE MATHEMATIK (2017)

Article Mathematics, Applied

Some Estimates for Virtual Element Methods

Susanne C. Brenner et al.

COMPUTATIONAL METHODS IN APPLIED MATHEMATICS (2017)

Article Mathematics, Interdisciplinary Applications

Arbitrary order 2D virtual elements for polygonal meshes: part II, inelastic problem

E. Artioli et al.

COMPUTATIONAL MECHANICS (2017)

Article Mathematics, Interdisciplinary Applications

Arbitrary order 2D virtual elements for polygonal meshes: part I, elastic problem

E. Artioli et al.

COMPUTATIONAL MECHANICS (2017)

Article Mathematics, Applied

THE NONCONFORMING VIRTUAL ELEMENT METHOD

Blanca Ayuso de Dios et al.

ESAIM-MATHEMATICAL MODELLING AND NUMERICAL ANALYSIS (2016)

Article Engineering, Multidisciplinary

A Virtual Element Method for elastic and inelastic problems on polytope meshes

L. Beirao da Veiga et al.

COMPUTER METHODS IN APPLIED MECHANICS AND ENGINEERING (2015)

Article Engineering, Multidisciplinary

On the Virtual Element Method for three-dimensional linear elasticity problems on arbitrary polyhedral meshes

Arun L. Gain et al.

COMPUTER METHODS IN APPLIED MECHANICS AND ENGINEERING (2014)

Article Mathematics, Applied

The Hitchhiker's Guide to the Virtual Element Method

L. Beirao da Veiga et al.

MATHEMATICAL MODELS & METHODS IN APPLIED SCIENCES (2014)

Article Mathematics, Applied

Equivalent projectors for virtual element methods

B. Ahmad et al.

COMPUTERS & MATHEMATICS WITH APPLICATIONS (2013)

Article Mathematics, Applied

BASIC PRINCIPLES OF VIRTUAL ELEMENT METHODS

L. Beirao da Veiga et al.

MATHEMATICAL MODELS & METHODS IN APPLIED SCIENCES (2013)

Article Mathematics, Applied

VIRTUAL ELEMENTS FOR LINEAR ELASTICITY PROBLEMS

L. Beirao da Veiga et al.

SIAM JOURNAL ON NUMERICAL ANALYSIS (2013)

Article Mathematics, Applied

Hitchhiker's guide to the fractional Sobolev spaces

Eleonora Di Nezza et al.

BULLETIN DES SCIENCES MATHEMATIQUES (2012)

Article Mathematics, Applied

T-coercivity: Application to the discretization of Helmholtz-like problems

Patrick Ciarlet

COMPUTERS & MATHEMATICS WITH APPLICATIONS (2012)

Article Computer Science, Interdisciplinary Applications

PolyMesher: a general-purpose mesh generator for polygonal elements written in Matlab

Cameron Talischi et al.

STRUCTURAL AND MULTIDISCIPLINARY OPTIMIZATION (2012)

Article Mathematics, Applied

Time harmonic wave diffraction problems in materials with sign-shifting coefficients

A. S. Bonnet-Ben Dhia et al.

JOURNAL OF COMPUTATIONAL AND APPLIED MATHEMATICS (2010)

Article Engineering, Multidisciplinary

Gmsh: A 3-D finite element mesh generator with built-in pre- and post-processing facilities

Christophe Geuzaine et al.

INTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN ENGINEERING (2009)