Boundary element methods in diffraction of a point-source acoustic wave by a rigid infinite wedge

Abstract The paper presents some boundary element methods (BEM) applied to diffraction of the harmonic acoustic wave generated by a point source. The authors first consider a basic boundary integral equation (BIE). Its analytical analysis permits development of some explicit conclusions. Then, some boundary element methods arise as a result of the dicretization of the BIE by various quadrature formulas. The matrices of the arising systems of linear algebraic equations (SLAE) are studied in the aspect of the structure of their spectrum. It is shown that the spectrum of the matrices is located in the right half-plane, hence the matrices are positive-definite. This predetermines a rapid convergence of the iterative algorithms applied, to solve the SLAEs.