Finite element approximation of a displacement formulation for time-domain elastoacoustic vibrations

Bermúdez, Alfredo; Rodrı́guez, Rodolfo; Santamarina, Duarte

doi:10.1016/s0377-0427(02)00694-5

Cited by 22 publications

(26 citation statements)

References 4 publications

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“…A rigorous mathematical error analysis for the purely linear case is provided in [2] for the case of matching grids which could be extended to the non-matching situation. There, due to the displacement-based formulation, the weak form of the subproblem for the fluid is an H div -problem requiring a non-standard discretization by means of Raviart-Thomas finite elements.…”

Section: Nonlinear Elastic/linear Acoustic Continuous Systemmentioning

confidence: 99%

A multiplicative Schwarz method and its application to nonlinear acoustic-structure interaction

2009

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Abstract.A new Schwarz method for nonlinear systems is presented, constituting the multiplicative variant of a straightforward additive scheme. Local convergence can be guaranteed under suitable assumptions. The scheme is applied to nonlinear acoustic-structure interaction problems. Numerical examples validate the theoretical results. Further improvements are discussed by means of introducing overlapping subdomains and employing an inexact strategy for the local solvers.

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Section: Nonlinear Elastic/linear Acoustic Continuous Systemmentioning

confidence: 99%

A multiplicative Schwarz method and its application to nonlinear acoustic-structure interaction

2009

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“…Now, within the domain s the partial differential equation for the mechanical field (see (1)), within the domain f the partial differential equation for the acoustic field (see (5)) and along the interface I the coupling conditions according to (12) and (13) have to be satisfied. Transforming to the weak form without setting the boundary integral on I to zero, we obtain for the mechanical system and for the acoustic system…”

Section: Coupled Field Formulationmentioning

confidence: 99%

“…We remark that an alternative coupled problem can be derived when, instead of the potentialbased formulation, a displacement-based problem formulation is chosen also for the fluid domain. A rigorous mathematical error analysis is provided in Reference [5] for the case of matching grids which could be extended to the non-matching situation. There, due to the displacement-based formulation, the weak form of the subproblem for the fluid is an H divproblem requiring a non-standard discretization by means of Raviart-Thomas finite elements.…”

Section: Coupled Field Formulationmentioning

confidence: 99%

Elasto–acoustic and acoustic–acoustic coupling on non‐matching grids

Flemisch

Kaltenbacher

Wohlmuth

2006

Numerical Meth Engineering

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SUMMARYFlexible discretization techniques for the approximative solution of coupled wave propagation problems are investigated, focussing on aero-acoustic and elasto-acoustic coupling. In particular, the advantages of using non-matching grids are presented, when one subregion has to be resolved by a substantially finer grid than the other subregion. For the elasto-acoustic coupling, the problem formulation remains essentially the same as for the matching situation, while for the aero-acoustic coupling, the formulation is enhanced with Lagrange multipliers within the framework of mortar finite element methods. Several numerical examples are presented to demonstrate the flexibility and applicability of the approach.

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“…In particular, one can choose a formulation based on pressure [21], displacement potential [18], velocity potential [14], or on the vector-valued fluid displacements [3]. The last choice results in different Hilbert spaces for the weak formulations, namely, H 1 and H div .…”

Section: Introduction and Preliminary Resultsmentioning

confidence: 99%

“…It is well known that standard conforming Lagrangian finite elements possibly result in poor accuracy if applied to H div settings. Thus, different finite element spaces for the subdomain discretizations have to be used for a pure displacement formulation [3]. This can be avoided by selecting as primary variables the mechanical displacement and the acoustic velocity potential.…”

Section: Introduction and Preliminary Resultsmentioning

confidence: 99%

The Equivalence of Standard and Mixed Finite Element Methods in Applications to Elasto-Acoustic Interaction

Flemisch¹,

Triebenbacher²,

Wohlmuth³

2010

SIAM J. Sci. Comput.

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Two commonly used problem formulations for the description of acoustic wave propagation are investigated; one is based on fluid displacement, and the other one is based on the velocity potential as the primary variable. Their equivalence under general Neumann boundary conditions is shown on both the continuous and the discrete level. To obtain the equivalence in the discrete setting, a nonstandard mixed finite element formulation is introduced. Thus, the transfer of an already available analysis for coupled elasto-acoustic problems in the displacement formulation to the potential formulation can be achieved. For the applications, the potential formulation is of special interest because it allows the use of standard Lagrangian elements in both the stucture and the fluid subdomain. Moreover, the approach does not require any conformity of the subdomain meshes at the interface, which considerably simplifies the physics-adapted mesh generation. Several engineering examples demonstrate the applicability and efficiency of the resulting numerical scheme.

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Finite element approximation of a displacement formulation for time-domain elastoacoustic vibrations

Cited by 22 publications

References 4 publications

A multiplicative Schwarz method and its application to nonlinear acoustic-structure interaction

A multiplicative Schwarz method and its application to nonlinear acoustic-structure interaction

Elasto–acoustic and acoustic–acoustic coupling on non‐matching grids

The Equivalence of Standard and Mixed Finite Element Methods in Applications to Elasto-Acoustic Interaction

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