INTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN ENGINEERING Int. J. Numer. Meth. Engng 2012; 91:27–38 Published online 30 May 2012 in Wiley Online Library (wileyonlinelibrary.com). DOI: 10.1002/nme.4251 Structural-acoustic coupling on non-conforming meshes with quadratic shape functions Herwig Peters 1, * ,† , Steffen Marburg 2 and Nicole Kessissoglou 1 1 School of Mechanical & Manufacturing Engineering, The University of New South Wales, Sydney, NSW 2052, Australia 2 LRT4 – Institute of Mechanics, Universität der Bundeswehr München, D-85579 Neubiberg, Germany SUMMARY Fully coupled finite element/boundary element models are a popular choice when modelling structures that are submerged in heavy fluids. To achieve coupling of subdomains with non-conforming discretizations at their common interface, the coupling conditions are usually formulated in a weak sense. The coupling matrices are evaluated by integrating products of piecewise polynomials on independent meshes. The case of interfacing elements with linear shape functions on unrelated meshes has been well covered in the litera- ture. This paper presents a solution to the problem of evaluating the coupling matrix for interfacing elements with quadratic shape functions on unrelated meshes. The isoparametric finite elements have eight nodes (Serendipity) and the discontinuous boundary elements have nine nodes (Lagrange). Results using linear and quadratic shape functions on conforming and non-conforming meshes are compared for an example of a fluid-loaded point-excited sphere. It is shown that the coupling error decreases when quadratic shape functions are used. Copyright © 2012 John Wiley & Sons, Ltd. Received 13 September 2011; Revised 9 November 2011; Accepted 14 November 2011 KEY WORDS: FE/BE coupling; acoustic structure interaction; quadratic shape function 1. INTRODUCTION The computational investigation of fully-coupled structural-acoustic interaction problems requires the coupling of two or more subdomains. The simplest case considers a fluid subdomain and a structural subdomain. The subdomains have to exchange information across their interface to rep- resent their physical interaction. The fluid pressure acts as an additional load on the structure (condition #1), whereas the structural displacement determines the particle velocity of the fluid at the wetted surface of the structure (condition #2). It is often desirable to discretize the computational subdomains independently to optimise their computational representation. However, this generally causes the two meshes to be non-conforming at their common interface. A number of approaches have been developed to deal with non- conforming meshes, for example, the Mortar method that was first proposed by Bernardi et al. [1]. Here, the coupling conditions at the common interface of the two subdomains are fulfilled in a weak sense. However, the convenience of coupling two independently discretized subdomains comes at a cost. On a matrix equation level, it requires the computation of coupling matrices, which are calcu- lated by integration of products of functions on generally unrelated meshes [2]. Typical algorithms for this task are described in articles by Puso [3], Flemisch et al. [4] and Heinstein and Laursen [5]. *Correspondence to: Herwig Peters, School of Mechanical & Manufacturing Engineering, The University of New South Wales, Sydney, NSW 2052, Australia. † E-mail: herwig.peters@student.unsw.edu.au Copyright © 2012 John Wiley & Sons, Ltd.