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Volume 118, Issue 4, October 2005
- STRUCTURAL ACOUSTICS AND VIBRATION 
118(2005); http://dx.doi.org/10.1121/1.2011151View Description Hide Description
In a series of pioneering papers, Burnett and Holford presented the formulation and numerical implementation of three-dimensional acoustic infinite elements for modeling acoustic fields in exterior unbounded domains surrounding a structure. They are all based on a multipole expansion outside a closed coordinate surface that circumscribes the structure; the multipole expansion has a radial variable , and two angular variables that describe the surfaces. In the finite element representation, the pressure field is discretized using a product of radial and angular shape functions. The angular variables are discretized directly using nodal angular values. However, in some cases, and especially in problems involving symmetry, nodes are located in certain positions where one of the angular variables is undefined, thus leading to errors in the value of the angular variable in the interior of the elements connected to these nodes, and hence in the computed acoustic field. To overcome this problem, we propose an alternative numerical formulation in this work, which is based on the interpolation of the position vector expressed in the global Cartesian coordinate system (as in conventional finite elements) instead of the interpolation of angular variables. We present numerical solutions for a few benchmark problems using the proposed method.