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    Directly Derived Non-Hyper-Singular Boundary Integral Equations for Acoustic Problems, and Their Solution through Petrov-Galerkin Schemes

    Z.Y. Qian1, Z.D. Han1, S.N. Atluri1

    CMES-Computer Modeling in Engineering & Sciences, Vol.5, No.6, pp. 541-562, 2004, DOI:10.3970/cmes.2004.005.541

    Abstract 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… More >

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