Author(s)

ANTONIO ROMERO, ROCIO VELÁZQUEZ-MATA, ANTONIO TADEU, PEDRO GALVÍN

Abstract

This paper proposes a general formulation of the BEM based on the Burton–Miller method to study scattering wave propagation by null-thickness bodies with complex geometry. This approach allows the use of arbitrary high-order elements and exact boundary geometry. 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 g eneralised Lagrange interpolation functions that are used as element shape functions. The proposed procedure consists of a new quadrature rule for the accurate evaluation of integral kernels in the sense of the Cauchy principal and the Hadamard finite part by an exclusively numerical procedure.

Keywords

hypersingular formulation, dual BEM, boundary integral equation, hypersingular kernels, singular kernels.