Z.Y. Qian1, Z.D. Han1, P. Ufimtsev1, S.N. Atluri1
CMES-Computer Modeling in Engineering & Sciences, Vol.6, No.2, pp. 133-144, 2004, DOI:10.3970/cmes.2004.006.133
Abstract The weak-form of Helmholtz differential equation, in conjunction with vector test-functions (which are gradients of the fundamental solutions to the Helmholtz differential equation in free space) is utilized as the basis in order to directly derive non-hyper-singular boundary integral equations for the velocity potential, as well as its gradients. Thereby, the presently proposed boundary integral equations, for the gradients of the acoustic velocity potential, involve only O(r−2) singularities at the surface of a 3-D body. Several basic identities governing the fundamental solution to the Helmholtz differential equation for velocity potential, are also derived for the further More >
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