TY - EJOU
AU - Qian, Z.Y.
AU - Han, Z.D.
AU - Atluri, S.N.
TI - Directly Derived Non-Hyper-Singular Boundary Integral Equations for Acoustic Problems, and Their Solution through Petrov-Galerkin Schemes
T2 - Computer Modeling in Engineering \& Sciences
PY - 2004
VL - 5
IS - 6
SN - 1526-1506
AB - Novel non-hyper-singular [i.e., only strongly-singular] boundary-integral-equations for the gradients of the acoustic velocity potential, involving only *O(r*^{−2}) singularities at the surface of a 3-D body, are derived, for solving problems of acoustics governed by the Helmholtz differential equation. The gradients of the fundamental solution to the Helmholtz differential equation for the velocity potential, are used in this derivation. Several basic identities governing the fundamental solution to the Helmholtz differential equation for velocity potential, are also derived. Using these basic identities, the strongly singular integral equations for the potential and its gradients [denoted here as φ-BIE, and q-BIE, respectively], are rendered to be only weakly-singular [i.e., possessing singularities of *O(r*^{−1}) at the surface of a 3-D body]. These weakly-singular equations are denoted as R-φ-BIE, and R-q-BIE, respectively. General Petrov-Galerkin
weak-solutions of R-φ-BIE, and R-q-BIE are discussed; and special cases of collocation-basedboundary-element numerical approaches [denoted as BEM-R-φ-BIE, and BEM-R-q-BIE], as well as Symmetric Galerkin Boundary Element approaches [denoted as SGBEM-R-φ-BIE and SGBEM-R-q-BIE, respectively] are also presented. The superior accuracy and efficiency of the SGBEM-R-φ-BIE and SGBEM-R-q-BIE are illustrated, through examples involving acoustic radiation as well as scattering from 3-D bodies possessing smooth surfaces, as well as surfaces with sharp corners.
KW - Boundary integral equations
KW - hypersingularity
KW - Petrov-Galerkin
DO - 10.3970/cmes.2004.005.541