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A modal synthesis method for the elastoacoustic vibration problem

Alfredo Bermúdez, Luis Hervella-Nieto, Rodolfo Rodríguez (2010)

ESAIM: Mathematical Modelling and Numerical Analysis

A modal synthesis method to solve the elastoacoustic vibration problem is analyzed. A two-dimensional coupled fluid-solid system is considered; the solid is described by displacement variables, whereas displacement potential is used for the fluid. A particular modal synthesis leading to a symmetric eigenvalue problem is introduced. Finite element discretizations with Lagrangian elements are considered for solving the uncoupled problems. Convergence for eigenvalues and eigenfunctions is proved,...

A modal synthesis method for the elastoacoustic vibration problem

Alfredo Bermúdez, Luis Hervella-Nieto, Rodolfo Rodríguez (2002)

ESAIM: Mathematical Modelling and Numerical Analysis - Modélisation Mathématique et Analyse Numérique

A modal synthesis method to solve the elastoacoustic vibration problem is analyzed. A two-dimensional coupled fluid-solid system is considered; the solid is described by displacement variables, whereas displacement potential is used for the fluid. A particular modal synthesis leading to a symmetric eigenvalue problem is introduced. Finite element discretizations with lagrangian elements are considered for solving the uncoupled problems. Convergence for eigenvalues and eigenfunctions is proved, error...

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

Roland Ernst, Bernd Flemisch, Barbara Wohlmuth (2009)

ESAIM: Mathematical Modelling and Numerical Analysis

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.

A note on poroacoustic traveling waves under Darcy's law: Exact solutions

P. M. Jordan, J. K. Fulford (2011)

Applications of Mathematics

A mathematical analysis of poroacoustic traveling wave phenomena is presented. Assuming that the fluid phase satisfies the perfect gas law and that the drag offered by the porous matrix is described by Darcy's law, exact traveling wave solutions (TWS)s, as well as asymptotic/approximate expressions, are derived and examined. In particular, stability issues are addressed, shock and acceleration waves are shown to arise, and special/limiting cases are noted. Lastly, connections to other fields are...

Accurate and online-efficient evaluation of the a posteriori error bound in the reduced basis method

Fabien Casenave, Alexandre Ern, Tony Lelièvre (2014)

ESAIM: Mathematical Modelling and Numerical Analysis - Modélisation Mathématique et Analyse Numérique

The reduced basis method is a model reduction technique yielding substantial savings of computational time when a solution to a parametrized equation has to be computed for many values of the parameter. Certification of the approximation is possible by means of an a posteriori error bound. Under appropriate assumptions, this error bound is computed with an algorithm of complexity independent of the size of the full problem. In practice, the evaluation of the error bound can become very sensitive...

Analysis of a coupled BEM/FEM eigensolver for the hydroelastic vibrations problem

Mauricio A. Barrientos, Gabriel N. Gatica, Rodolfo Rodríguez, Marcela E. Torrejón (2010)

ESAIM: Mathematical Modelling and Numerical Analysis

A coupled finite/boundary element method to approximate the free vibration modes of an elastic structure containing an incompressible fluid is analyzed in this paper. The effect of the fluid is taken into account by means of one of the most usual procedures in engineering practice: an added mass formulation, which is posed in terms of boundary integral equations. Piecewise linear continuous elements are used to discretize the solid displacements and the fluid-solid interface variables....

Analysis of a coupled BEM/FEM eigensolver for the hydroelastic vibrations problem

Mauricio A. Barrientos, Gabriel N. Gatica, Rodolfo Rodríguez, Marcela E. Torrejón (2004)

ESAIM: Mathematical Modelling and Numerical Analysis - Modélisation Mathématique et Analyse Numérique

A coupled finite/boundary element method to approximate the free vibration modes of an elastic structure containing an incompressible fluid is analyzed in this paper. The effect of the fluid is taken into account by means of one of the most usual procedures in engineering practice: an added mass formulation, which is posed in terms of boundary integral equations. Piecewise linear continuous elements are used to discretize the solid displacements and the fluid-solid interface variables. Spectral...

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