Boundary Element Method fails to provide a unique solution for exterior problems at frequencies corresponding to internal resonances; this is the well-known non-uniqueness problem. This problem becomes even more critical at higher frequencies with the increasing modal density inside the cavity. Approaches have been developed to circumvent this limitation as the over determination points or the Burton-Miller formulation in Direct BEM. In Indirect BEM, the most commonly used approach consists in applying some absorption (Robin boundary conditions) inside the cavity to damp those internal resonances. Nevertheless, the approach has a large computational cost as it increases the number of unknowns. In this paper we show that imposing Robin boundary condition only on certain percentage of elements allows to mitigate the non-uniqueness problem without drastically increase the computational cost. Numerical examples on industrial size problem using both standard IBEM and Fast Multipole BEM are presented to demonstrate the accuracy of the solution over the entire range of frequencies. Finally, equivalence with the Burton and Miller method for direct formulation is demonstrated.

Mitigation of the Non-uniqueness Problem for the Indirect Boundary Element Method / M. Pierini; R. D'Amico; A. Pratellesi; M. Tournour. - STAMPA. - (2010), pp. 0-0. (Intervento presentato al convegno 10th International Conference, Recent Advances in Structural Dynamics 2010 tenutosi a Southampton, UK nel 12-14 July 2010).

### Mitigation of the Non-uniqueness Problem for the Indirect Boundary Element Method

#### Abstract

Boundary Element Method fails to provide a unique solution for exterior problems at frequencies corresponding to internal resonances; this is the well-known non-uniqueness problem. This problem becomes even more critical at higher frequencies with the increasing modal density inside the cavity. Approaches have been developed to circumvent this limitation as the over determination points or the Burton-Miller formulation in Direct BEM. In Indirect BEM, the most commonly used approach consists in applying some absorption (Robin boundary conditions) inside the cavity to damp those internal resonances. Nevertheless, the approach has a large computational cost as it increases the number of unknowns. In this paper we show that imposing Robin boundary condition only on certain percentage of elements allows to mitigate the non-uniqueness problem without drastically increase the computational cost. Numerical examples on industrial size problem using both standard IBEM and Fast Multipole BEM are presented to demonstrate the accuracy of the solution over the entire range of frequencies. Finally, equivalence with the Burton and Miller method for direct formulation is demonstrated.
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2010
10th International Conference, Recent Advances in Structural Dynamics 2010
Southampton, UK
12-14 July 2010
M. Pierini; R. D'Amico; A. Pratellesi; M. Tournour
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Utilizza questo identificatore per citare o creare un link a questa risorsa: `https://hdl.handle.net/2158/393096`