title: The Partition of Unity Finite Element Method for the simulation of waves in air and poroelastic media.
abstract: Recently Chazot et al. [J. Sound Vib. 332, 1918-1929 (2013)] applied the Partition of Unity Finite Element Method for the analysis of interior sound fields with absorbing materials. The method was shown to allow a substantial reduction of the number of degrees of freedom compared to the standard Finite Element Method. The work is however restricted to a certain class of absorbing materials that react like an equivalent fluid. This paper presents an extension of the method to the numerical simulation of Biot's waves in poroelastic materials. The technique relies mainly on expanding the elastic displacement as well as the fluid phase pressure using sets of plane waves which are solutions to the governing partial differential equations. To show the interest of the method for tackling problems of practical interests, poroelastic-acoustic coupling conditions as well as fixed or sliding edge conditions are presented and numerically tested. It is shown that the technique is a good candidate for solving noise control problems at medium and high frequency.
authors.affiliation: Université de Technologie de Compiègne, Laboratoire Roberval UMR 7337, CS 60319, 60203 Compiègne cedex, France.
authors.forename: Jean-Daniel
authors.initials: JD
authors.lastname: Chazot
authors.affiliation: Université de Technologie de Compiègne, Laboratoire Roberval UMR 7337, CS 60319, 60203 Compiègne cedex, France.
authors.forename: Emmanuel
authors.initials: E
authors.lastname: Perrey-Debain
authors.affiliation: Laboratoire d'Ingénierie des Systèmes Mécaniques et des Matériaux (LISMMA), SUPMECA, 3 rue Fernand Hainaut, 93407 Saint-Ouen, France.
authors.forename: Benoit
authors.initials: B
authors.lastname: Nennig