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Empowering Human Decision-Making in AI Models: The Path to Trust and Transparency
Open Access
ARTICLE
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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