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

This work formulates the singularity-free integral equations to study 2-D a coustic scattering problems. To avert the nonuniqueness difficulties, Burto n's and Burton and Miller's methods are employed to solve the Dirichlet and Neumann problems, respectively. The surface Helmholtz integral equations a nd their normal derivative equations in bounded form are derived. The weakl y singular integrals are desingularized by subtracting a term from the inte grand and adding it back with an exact value. Depending on the relevant pro blem, the additional integral can finally be either expressed in an explici t form or transformed to form a surface source distribution of the related equipotential body. The hypersingular kernel is desingularized further usin g some properties of an interior Laplace problem. The new formulations are advantageous in that they can be computed by directly using standard quadra ture formulas. Also discussed is the Gamma-contour, a unique feature of 2-D problems. Instead of dividing the boundary surface into several small elem ents, a parametric representation of a 2-D boundary curve is further propos ed 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 p roposed method's effectiveness. (C) 1999 Acoustical Society of America. [S0 001-4966(99)03401-X].