On the coupling of the Curved Virtual Element Method with the one-equation Boundary Element Method for 2D exterior Helmholtz problems

by   Luca Desiderio, et al.

We consider the Helmholtz equation defined in unbounded domains, external to 2D bounded ones, endowed with a Dirichlet condition on the boundary and the Sommerfeld radiation condition at infinity. To solve it, we reduce the infinite region, in which the solution is defined, to a bounded computational one, delimited by a curved smooth artificial boundary and we impose on this latter a non reflecting condition of boundary integral type. Then, we apply the curved virtual element method in the finite computational domain, combined with the one-equation boundary element method on the artificial boundary. We present the theoretical analysis of the proposed approach and we provide an optimal convergence error estimate in the energy norm. The numerical tests confirm the theoretical results and show the effectiveness of the new proposed approach.



There are no comments yet.


page 24

page 27


CVEM-BEM coupling with decoupled orders for 2D exterior Poisson problems

For the solution of 2D exterior Dirichlet Poisson problems we propose th...

Coupling of finite element method with boundary algebraic equations

Recently, a combined approach of CFIE--BAE has been proposed by authors ...

The Boundary Element Method of Peridynamics

The peridynamic theory reformulates the governing equation of continuum ...

Robin-Dirichlet alternating iterative procedure for solving the Cauchy problem for Helmholtz equation in an unbounded domain

We consider the Cauchy problem for the Helmholtz equation with a domain ...

Analysis of a Sinclair-type domain decomposition solver for atomistic/continuum coupling

The "flexible boundary condition method", introduced by Sinclair and cow...

The Virtual Element Method for a Minimal Surface Problem

In this paper we consider the Virtual Element discretization of a minima...
This week in AI

Get the week's most popular data science and artificial intelligence research sent straight to your inbox every Saturday.