WIT Press


A BEM BASED ON THE BÉZIER/BERNSTEIN POLYNOMIAL FOR ACOUSTIC WAVEGUIDE MODELIZATION

Price

Free (open access)

Paper DOI

10.2495/BE420021

Volume

126

Pages

11

Page Range

13 - 23

Published

2019

Size

2,103 kb

Author(s)

ANTONIO ROMÉRO, PEDRO GALVÍN, ANTÓNIO TADEU

Abstract

This paper proposes a novel boundary element approach formulated on the Bézier–Bernstein basis to yield a geometry-independent field approximation. The proposed method is geometrically based on both computer aided design (CAD) and isogeometric analysis (IGA), but field variables are independently approximated from the geometry. This approach allows the appropriate approximation functions for the geometry and variable field to be chosen. We use the Bézier–Bernstein form of a polynomial as an approximation basis to represent both geometry and field variables. The solution of the element interpolation problem in the Bézier–Bernstein space defines generalised Lagrange interpolation functions that are used as element shape functions. The resulting Bernstein–Vandermonde matrix related to the Bézier–Bernstein interpolation problem is inverted using the Newton–Bernstein algorithm. The applicability of the proposed method is demonstrated by solving the Helmholtz equation over an unbounded region in a two-and-a-half dimensional (2.5D) domain.

Keywords

subparametric method, Bézier–Bernstein curve, Newton–Bernstein algorithm, computer-aided design, isogeometric analysis