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Boundary element methods in diffraction of a point-source acoustic wave by a rigid infinite wedge. (English) Zbl 1464.76110

Summary: 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.

MSC:

76M15 Boundary element methods applied to problems in fluid mechanics
65N38 Boundary element methods for boundary value problems involving PDEs
76Q05 Hydro- and aero-acoustics

Software:

CRAIG; LSQR
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Full Text: DOI

References:

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