FEM Solution of Exterior Elliptic Problems with Weakly Enforced Integral Non Reflecting Boundary Conditions

Bertoluzza, Silvia; Falletta, Silvia

doi:10.1007/s10915-019-01048-4

Cited by 6 publications

(1 citation statement)

References 22 publications

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“…It is worth noting that it is possible in principle to decouple the CVEM and the BEM discretization, both in terms of degree of accuracy and of non-matching grids. This would lead to a non-conforming coupling approach by using, for example, a mortar type technique (see for instance [11]). Such an approach would offer the further advantage of coupling different types of approximation spaces and of using fast techniques for the discretization of the BEM (see for example the very recent papers [17,12,21,22]).…”

Section: Discussionmentioning

confidence: 99%

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

Desiderio¹,

Falletta²,

Ferrari³

et al. 2021

Preprint

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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.

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Section: Discussionmentioning

confidence: 99%

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

Desiderio¹,

Falletta²,

Ferrari³

et al. 2021

Preprint

View full text Add to dashboard Cite

show abstract

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

et al. 2022

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For the solution of 2D exterior Dirichlet Poisson problems, we propose the coupling of a Curved Virtual Element Method (CVEM) with a Boundary Element Method (BEM), by using decoupled approximation orders. We provide optimal convergence error estimates, in the energy and in the weaker $$\textit{L}^\text {2}$$ L 2 -norm, in which the CVEM and BEM contributions to the error are separated. This allows for taking advantage of the high order flexibility of the CVEM to retrieve an accurate discrete solution by using a low order BEM. The numerical results confirm the a priori estimates and show the effectiveness of the proposed approach.

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

Desiderio¹,

Falletta²,

Scuderi³

2021

Computers & Mathematics with Applications

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FEM Solution of Exterior Elliptic Problems with Weakly Enforced Integral Non Reflecting Boundary Conditions

Cited by 6 publications

References 22 publications

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

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

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

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

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