DeepAI
Log In Sign Up

A Virtual Element Method for the wave equation on curved edges in two dimensions

06/11/2021
by   Franco Dassi, et al.
0

In this work we present an extension of the Virtual Element Method with curved edges for the numerical approximation of the second order wave equation in a bidimensional setting. Curved elements are used to describe the domain boundary, as well as internal interfaces corresponding to the change of some mechanical parameters. As opposite to the classic and isoparametric Finite Element approaches, where the geometry of the domain is approximated respectively by piecewise straight lines and by higher order polynomial maps, in the proposed method the geometry is exactly represented, thus ensuring a highly accurate numerical solution. Indeed, if in the former approach the geometrical error might deteriorate the quality of the numerical solution, in the latter approach the curved interfaces/boundaries are approximated exactly guaranteeing the expected order of convergence for the numerical scheme. Theoretical results and numerical findings confirm the validity of the proposed approach.

READ FULL TEXT

page 20

page 21

page 22

page 23

07/27/2020

The Mixed Virtual Element Method on curved edges in two dimensions

In this work, we propose an extension of the mixed Virtual Element Metho...
11/18/2020

The mixed virtual element method for grids with curved interfaces

In many applications the accurate representation of the computational do...
03/06/2019

Geometry Mapping, Complete Pascal Scheme versus Standard Bilinear Approach

This paper presents a complete Pascal interpolation scheme for use in th...
11/20/2021

Bend 3d Mixed Virtual Element Method for Elliptic Problems

In this study, we propose a virtual element scheme to solve the Darcy pr...
09/11/2017

Complete Pascal Interpolation Scheme For Approximating The Geometry Of A Quadrilateral Element

This paper applies a complete parametric set for approximating the geome...
10/30/2020

Numerical solution of the wave propagation problem in a plate

In this work, the propagation of an ultrasonic pulse in a thin plate is ...
12/16/2021

Helmholtz equation and non-singular boundary elements applied to multi-disciplinary physical problems

The famous scientist Hermann von Helmholtz was born 200 years ago. Many ...