Higher-order discontinuous shape functions in boundary element codes.

Abstract

Boundary element codes for acoustics use shape functions to approximate the pressure and normal velocity over the surface of individual elements. Many codes use zeroth order or constant interpolation over each element. A consequence of constant interpolation is that the surface quantities are discontinuous between elements. Higher-order shape functions have also been used and lead to models which converge more quickly than those using constant interpolation. Usually, the interpolation makes use of nodal points located along the edges of an element and results in the surface quantities being continuous. There are two limitations that result from this requirement of continuity. First, allowing the surface quantities to be discontinuous between elements often improves the accuracy of the nodal values. Second, modeling sharp corners can be difficult since the normal direction is not uniquely defined. This paper discusses the use of higher-order discontinuous shape functions where the collocation points are located on the interior of the element. Using several 2-D and 3-D examples, the accuracy and convergence of this technique is evaluated and shown to be superior to models using constant or continuous shape functions.