A boundary integral equation method for two-dimensional acoustic scattering problems

This work formulates the singularity-free integral equations to study 2-D acoustic scattering problems. To avert the nonuniqueness difficulties, Burton's and Burton and Miller's methods are employed to solve the Dirichlet and Neumann problems, respectively. The surface Helmholtz integral equations and their normal derivative equations in bounded form are derived. The weakly singular integrals are desingularized by subtracting a term from the integrand and adding it back with an exact value. Depending on the relevant problem, the additional integral can finally be either expressed in an explicit form or transformed to form a surface source distribution of the related equipotential body. The hypersingular kernel is desingularized further using some properties of an interior Laplace problem. The new formulations are advantageous in that they can be computed by directly using standard quadrature formulas. Also discussed is the Gamma-contour, a unique feature of 2-D problems. Instead of dividing the boundary surface into several small elements, a parametric representation of a 2-D boundary curve is further proposed to facilitate a global numerical implementation. Calculations consist of acoustic scattering by a hard and a soft circular cylinder, respectively. Comparing the numerical results with the exact solutions demonstrates the proposed method's effectiveness. (C) 1999 Acoustical Society of America. [S0001-4966(99)03401-X].